The book’s name:
The Tafsir of Ath-Thaʿlabiyy is known as "Al-Kashf wa Al-Bayān ʿan Tafsir Al-Qurʾān" which is definitively proven without the slightest doubt. This is due to many strong and mutually reinforcing evidences including the following:
1-Ath-Thaʿlabiyy himself, may Allah have mercy upon him, stated in the introduction to his Tafsir  that he gave it this name, as he said: “I named it: "Al-Kashf wa Al-Bayān ʿan Tafsir Al-Qurʾān". 
If this was the only evidence, it would be sufficient, so how would be the case if we add the following evidences: 
2-His close student and narrator of his Tafsir, Abū Al-Ḥasan Al-Wāhidiyy also gave him this name
as he said in the introduction to his Tafsir "Al-Basīṭ" in the context of his praise of his shaykh Ath-Thaʿlabiyy: “He wrote the Tafsir entitled "Al-Kashf wa Al-Bayān ʿan Tafsir Al-Qurʾān".
3-Those who narrated this Tafsir with the chain of transmission on the authority of Ath-Thaʿlabiyy referred to it in their narration as "Al-Kashf wa Al-Bayān ʿan Tafsir Al-Qurʾān", and among them are:
A - Ibn Khayr Al-Ishbīliyy (d. 575 AH) in the index of what he narrated on the authority of his shaykhs. 
B - ʿIzz Ad-Dīn ibn Al-Athīr (d. 630 AH) in his book "Usd Al-Ghābah". 
4- This name is found on the written copies of the book, 
and books that listed manuscripts of Tafsir books, such as the History of Arabic Literature by Brockelmann, and the Comprehensive Index to the Arabic-Islamic Manuscript Heritage.
5-It was mentioned by this name in books authored on listing the names of books and branches of knowledge like "Kashf Aẓ- Ẓunūn, Hadiyyat ʿArrāfīn and Muʿjam Al-Muʾallifīn". In this way, the previous evidences proved to us beyond any doubt that the name of this Tafsir is "Al-Kashf wa Al-Bayān ʿan Tafsir Al-Qurʾān".
Proving the book’s attribution to its author.
After it was proven to us that the name of the Tafsir of Ath-Thaʿlabiyy is "Al-Kashf wa Al-Bayān ʿan Tafsir Al-Qurʾān", we come to prove the attribution of this book to Imam Ath-Thaʿlabiyy.
So we say: The attribution of this book to Ath-Thaʿlabiyy is firmly established through strong evidence and clear proofs, which prove that this Tafsir is written by Ath-Thaʿlabiyy, which becomes a clear and well-known matter that does not accept argument or disagreement.
Among the proofs of attributing Al-Kashf wa Al-Bayān to Imam Ath-Thaʿlabiyy are the following:
1-The book is narrated with a connected chain of transmission back to its author. Among those who narrated it are:
A- Abū Al-Ḥasan Al-Wāhidiyy, the famous student of Imam Ath-Thaʿlabiyy and the narrator of his Tafsir.
In the Maḥmūdiyyah copy, which is the original copy for Al-Kashf wa Al-Bayān, a continuous chain of narrators was mentioned, narrated by the prominent reciter Abū ʿImrān Mūsā ibn ʿAliyy ibn Al-Ḥasan Al-Jazariyy, on the authority of his shaykh, Imam, the Hāfiẓ Abū Muḥammad ʿAbdullah ibn ʿAliyy At-Tikrītiyy in Shawwāl of the year five hundred and eighty-one (581 AH). He said: “The shaykh and imam Abū Al-Faḍl ibn Abi Al-Khayr Al-Yamani, said: “Imam Abū Al-Ḥasan ʿAliyy ibn Aḥmad Al-Wāḥidi said: “The author Abū Isḥāq Ath-Thaʿlabi informed us…”
B- The Tafsir was narrated from another way on the authority of Al-Wāḥidi as well, as Ibn Khayr Al-Ishbīliyy narrated it in "Fahrasatu mā Rawāhu ʿan Shuyūkhihi" on the authority of his shaykh, Al-Qāḍī ʿIyāḍ with his chain of transmission to Al-Wāḥidi on the authority of Ath-Thaʿlabiyy. Al-Ishbīlī said: “The book of Al-Kashf wa Al-Bayān ʿan Tafsir Al-Qurʾān, authored by Professor Abū Isḥāq Aḥmad ibn Muḥammad Ath-Thaʿlabiyy, may Allah have mercy upon him, was narrated to me by Al- Qāḍī Abū Al-Faḍl ʿIyāḍ ibn Mūsā ibn ʿIyāḍ Al-Yaḥsubiyy, may Allah have mercy upon him. He said: ‘Shaykh Abu Said Haydar ibn Yahya ibn Haydar ibn Yahya l-Hanbaliyy As-Sufiyy the resident of Makka narrated it to me by way of Ijāzah (authorization), among what he wrote to me by his own hand in Makkah as he said: ‘Al-Qādi Abu Al-Maḥāsin ʿAbd Al-Wāhid ibn Ismā’il Ar-Rūyāniyy related via Abū Al-Hasan ʿAliyy ibn Aḥmad Al-Wāḥidi via Abū Isḥāq Aḥmad ibn Muḥammad Ath-Thaʿlabiyy, its author.’
C- This Tafsir was also narrated by Imam Abū Muḥammad Al-Baghawiyy in his book "Maʿālim At-Tanzīl" via Ath-Thaʿlabiyy’s student Abū Saʿīd Ash-Shurayhiyy Al-Khawārizmiyy. He said in the introduction of his Tafsir: “Most of what I quoted in it of commentary on the authority of ʿAbdullah ibn ʿAbbās, may Allah be pleased with them both, the outstanding scholar of this nation, and those after him from the followers and imams of the predecessors, was part of what Shaykh Abū Saʿīd Ash-Shurayhiyy Al-Khawārizmiyy related to me on the authority of Professor Abū Isḥāq Aḥmad ibn Muḥammad ibn Ibrāhim ATh-Thaʿlabiyy on the authority of his shaykhs. Then he mentioned the relevant chains of transmission.
D- Among those who narrated this Tafsir with a chain of transmission connected to its author, Imam ʿIzz Ad-Dīn Ibn Al-Athīr in his book Usd Al-Ghābah where he mentioned in the introduction to his book the great books from which he narrated hadiths and others, and mentioned in the first of these books the Tafsir of Ath-Thaʿlabiyy. Then he included his narration of this book on the authority of Ahmad ibn Khalaf Ash-Shīrāzī, who was the student of Ath-Thaʿlabiyy. He said: I was informed by Abū Al-ʿAbbās Aḥmad ibn ʿUthmān ibn Abi ʿAliyy ibn Mahdi Al-Zarzāri, the righteous shaykh, may Allah have mercy upon him, that Masʿūd ibn Al-Ḥasan ibn Al-Qāsim Al-Asbahāni and Abū ʿAbdullah Al- Ḥasan ibn Al-ʿAbbās Ar-Rustumi both said: Aḥmad ibn Khalaf Ash-Shīrāzi said that Abū Isḥāq Aḥmad ibn Muḥammad ibn Ibrāhīm Ath-Thaʿlabiyy reported to us all the book of Al-Kashf wa Al-Bayān fi Tafsir Al-Qurʾān. I heard it from him from the beginning of the book to the end of Surat Al-Nisāʾ. As for the rest of the book I listened to some parts of it and had Ijāzah for some parts.
E-The book was also narrated by Al-Hāfiz Ibn Hajar Al-ʿAsqalāni (d. 852), the famous imam, in his book "Al-Muʿjam Al-Mufahras", in which he mentioned his narrations of the famous books, and the separate parts.
He narrated the Tafsir of Ath-Thaʿlabi on the authority of his student: Abū Saʿīd Al-Firrukhrādhi. Ibn Ḥajar, may Allah have mercy upon him, said: “The book of "Al-Kashf wa Al-Bayān fi Tafsir Al-Qurʾān by Abū Isḥāq Ath-Thaʿlabiyy. Al-Kamāl Aḥmad ibn ʿAliyy ibn ʿAbd Al-Ḥaqq informed us via direct verbal contact on the authority of Al-Ḥāfiz Abū Al-Ḥajjāj Al-Mizzi and Muḥammad Al-Qāsim ibn Muḥammad Al-Barzāli. Abū Al-Ḥasan ʿAliyy ibn Aḥmad ibn ʿAbd Al-Wāḥid ibn Al-Bukhāri related to us by way of Ijāzah, if not by recitation, on the authority of Manṣūr ibn ʿAbd Al-Munʿim and ʿAbdullah ibn ʿUmar Aṣ-Ṣaffār and Al-Muʾayyad Aṭ-Ṭūsi that Abu Muḥammad Al-ʿAbbās ibn Muḥammad ibn Abi Manṣūr Al-ʿAṣṣāri Aṭ-Ṭūsi, knows as ʿAbbāsah informed that Abū Saʿīd Muḥammad ibn Saʿīd ibn Muḥammad ibn Firrukhrādh related that Abū Isḥāq Aḥmad ibn Muḥammad ibn Ibrāhīm An-Naysābūrī Ath-Thaʿlabi related that book to them.”
F-Among those who narrated this book is the student of Abu Maʿshar ʿAbd Al-Karim ibn ʿAbd As-Samad Al-Qattan (d.478 AH), as reported by As-Subki in Tabaqat Ash-Shāfiʿiyyah where he said: “He narrated the Tafsir of Ath-Thaʿlabiyy on the authority of its author.”
2- Among the proofs of the attribution of this commentary to Ath-Thaʿlabi is the scholars’ agreement to benefit from it, either by quoting from it, abbreviating it, or the like, which will be discussed in detail when speaking about the importance of the book in the fourth topic.
3-Another proof is the wide fame of attributing this commentary to Ath-Thaʿlabi. You will hardly find a mention of Ath-Thaʿlabi in the books of biographers, unless it is associated with his Tafsir.
For example, ʿAbd Al-Ghāfir Al-Fārisiyy says about Ath-Thaʿlabiyy: “He is the author of glorious works, including his book of Tafsir that contains unique meanings and allusions, statements of trustworthy people, and multiple forms of parsing and Qirāʾāt. There is also his book: "Al-ʿArāʾis that is too famous to introduce.”
Yāqūt Al-Ḥamawiyy says about him: “He is the exegete, author of the book that is widely circulated, known as Tafsir Ath-Thaʿlabiyy.”
As-Suyuṭī: “He is the author of the well-known Tafsir.”
His student Al-Wāḥhidī: “He wrote the Tafsir entitled: Al-Kashf wa Al-Bayān ʿan Tafsir Al-Qurʾān.”
Al-Qifṭī: “He authored the renowned book of Tafsir.”
Ibn Khallikān: “He compiled the great book of Tafsir that surpassed all other books on that regard.”
Adh-Dhahabī: “He wrote the great book of Tafsir.”
Al-Isnawī: “He is the author of the known Tafsir.”
As-Subkī: “He is the author of the Tafsir.”
Thus, the mention of Ath-Thaʿlabiyy was associated with the mention of his Tafsir, which indicates that the book’s attribution to him is very famous. 
4- Added to the above proofs of the attribution of this Tafsir to Ath-Thaʿlabiyy, the multiple written copies of this book under the name of the book: Al-Kashf wa Al-Bayān ʿan Tafsir Al-Qurʾān, and the name of its author: Abū Isḥāq Aḥmad ibn Muḥammad Ath-Thaʿlabiyy. 
The foregoing evidences and proofs definitively prove the attribution of Al-Kashf wa Al-Bayān to Abū Isḥāq Ath-Thaʿlabiyy, may Allah have mercy upon him.