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Praise be to Allah.
Firstly:
We have previously discussed the issue of naming the mosque with one of the names of Allah, may He be glorified and exalted, such as Masjid ar-Rahmaan, Masjid al-Qudoos, Masjid as-Salaam. It is well-known that Allah, may He be glorified, says, and His word is decisive: “And the mosques are for Allah (Alone), so invoke not anyone along with Allah” [al-Jinn 72:18]. So all the mosques belong to Allah, may He be exalted, without exception; therefore naming a mosque by one of the names of Allah so as to identify it is a newly invented matter that was not done by people in the past, so it is better to refrain from doing that.
Secondly:
The basic principle is that there is nothing wrong with calling a mosque Masjid Ahl al-Hadith (Masjid e Ahle Hadis), because this is giving it a description which is Islamically acceptable. As this name is regarded by the scholars as something praiseworthy and good, calling the mosque by this name is something acceptable and there is nothing wrong with it, in sha Allah.
But this ruling is only with regard to principles and in general terms. Before applying it, however, in the case of your mosque, you should look at the situation in your country. If claiming to belong to Ahl al-Hadith and calling yourselves by their name, or calling your mosque by the name “Ahl al-Hadith”, will result in dividing the Muslim community, or creating resentment in their hearts, or reviving ignorant sectarianism and stirring up turmoil and trouble among the Muslims, then you should refrain from using this name. In fact you should even refrain from other, more important, permissible and recommended actions if that will result in any of these troubles. The most that can be said about giving your mosque this name is that it is something permissible that you have refrained from, and you have other options among permissible names that will bring people together and not cause division, that will attract people and not put them off, so that you will have no need of that name. The Prophet (blessings and peace of Allah be upon him) disapproved of using Islamically acceptable names if the motive behind it is to show devotion to something other than the truth.
For more information, please see the answers to questions no. 124196 and 12761.
Secondly:
If the matter is the opposite, and the congregation of the mosque are keen to keep the name of the mosque as Masjid Ahl al-Hadith or some other similar permissible name, then we do not think that there is anything wrong with that, and we do not think that the people in charge of the mosque should be stubborn in rejecting that wish and creating resentment in their brother’s hearts because of that, even though the name is originally something that is permissible, not obligatory or recommended, but it is a good and permissible name that is intended to distinguish the place from others, such as calling the mosque by the name of a tribe or neighbourhood or person and the like.
If not using this name will cause some resentment and may put off some closed-minded people among the congregation of the mosque from praying in it, then we do not think, in this case that you should be too strict with regard to the issue of naming the mosque, or change a name that people are used to, if changing the name will upset people or lead to shouting in the mosque, or put people off or alienate them, or stir up enmity among the Muslims.
If the congregation of the mosque can work out a solution among themselves and come to some agreement, there is nothing wrong with that; in fact any permissible things that bring about reconciliation between people and dispel resentment and grudges, are good and praiseworthy, and you should strive to achieve that, and not give the Shaytaan any way of causing trouble in your community.
And Allah knows best.