Praise be to Allah.
We have stated on more than one occasion that the names of Allah, may He be exalted, are a tawqeefi matter [i.e., they can only be known through divine Revelation and sound texts of hadeeth, with no room for ijtihaad], so it is not permissible to call Allah, may He be exalted, by any name other than those with which He named Himself or His Messenger (blessings and peace of Allah be upon him) named Him.
As stated previously, with regard to words which are mentioned in the Qur’an and Sunnah only by way of description or information, and it is not narrated that Allah is called by these names, it is not correct to call Him by them.
Undoubtedly if a person calls himself or someone else ‘Abd as-Saboor, what is meant by it is an expression of servitude to Allah, may He be exalted, and a belief that as-Saboor is one of the beautiful names of Allah, may He be glorified, because that is well-known among people and it is mentioned in the report that lists His beautiful names, that was narrated by at-Tirmidhi and others.
And we have previously stated it is not right to add any name that is not proven by a hadeeth from the Prophet (blessings and peace of Allah be upon him). See the answer to question no. 72318
But here we should differentiate between two scenarios that have to do with using the name ‘Abd as-Saboor
When a person wants to name his son or the son of someone else by this name. We say that this is disallowed, because there is no proven report concerning it. Hence more than one of the scholars refrained from including it among the beautiful names of Allah. Among the names proven in the Book of Allah and the Sunnah of His Messenger there are sufficient options, such that there is no need to use a name concerning which there is a difference of opinion as to whether it is proven or not.
When a person has been given this name by his family, and is well known by it among the people, and it is recorded in his official papers, then he finds out that there are some scholars who do not think that this name is one of the beautiful names of Allah. In this case it seems – and Allah knows best – that there is nothing wrong with him keeping this name, especially if it will be difficult for him to change his official papers which use this name. This is easier and may be overlooked. Moreover, the most that may be said concerning it is that there is no proof that this is one of the divine names; it cannot be said that it is proven that it is not one of the divine names. Rather the question of whether as-Saboor is one of the beautiful names of Allah remains a matter of ijtihaad and individual scholarly opinion, and it is proven in the hadeeth that Allah, may He be glorified and exalted, has the attribute of sabr (patience).
It was narrated that Abu Moosa al-Ash‘ari (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “No one is more patient in bearing offensive things that he hears than Allah, may He be glorified and exalted; others are associated with Him, a son is attributed to Him, but He still grants them health and provision.”
Narrated by al-Bukhaari (7378) and Muslim (2804).
Al-Khattaabi (may Allah have mercy on him) said:
As-Saboor is the One Who does not hasten to wreak vengeance upon the sinners; rather He delays that until an appointed time, and He gave them respite for a certain amount of time.
The meaning of the name as-Saboor, as a description of Allah, may He be glorified, is close to the meaning of the name al-Haleem (the Most Forbearing), except that the difference between the two is that in the case of as-Saboor, it does not imply that they are safe from punishment, whereas in the case of al-Haleem, it implies that they may be safe from it. And Allah knows best what is correct.
End quote from Sha’n ad-Da‘wah (98)
The name as-Saboor is mentioned among the beautiful names of Allah in the report of al-Waleed ibn Muslim that was narrated by at-Tirmidhi and others, as stated above. Other scholars who regarded it as one of the beautiful names of Allah are: al-Khattaabi, Ibn Mandah, al-Haleemi, al-Bayhaqi, Ibn al-‘Arabi, al-Qurtubi, Ibn al-Qayyim and others.
See: Mu‘taqad Ahl as-Sunnah wa’l-Jamaa‘ah fi Asma’ Allah al-Husna by Dr Muhammad Khaleefah at-Tameemi (223)
And Allah knows best.