All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
According to the view of the majority of scholars it is not permissible to use a (paint) brush which is made from the hair of pigs because it [the hair of pigs] is impure.
The prohibition of using it is even confirmed and the sin is even greater in writing the word "Allaah" or any of Allaah's Names with it.
Indeed, the Names of Allaah should be honored and glorified and not be subjected to what is impure. Allaah Says (what means): {That [is so]. And whoever honors the symbols [i.e. rites] of Allaah — indeed, it is from the piety of hearts.} [Quran 22:32] Allaah also Says (what means): {That [has been commanded], and whoever honors the sacred ordinances of Allaah — it is best for him in the sight of his Lord.} [Quran 22:30]
It should be noted here that some scholars like the scholars of the Hanafi School of jurisprudence, are of the view that it is disliked to write the Names of Allaah on walls and the like. The famous Hanafi book entitled Al-Haashiyah 'ala Radd Al-Muhtaar reads: “It is disliked to write the Quran and the Names of Allaah on dirhams [a kind of silver coin], on pulpits, on walls, and on things that are spread out [like a carpet or rug, for instance].”
Allaah Knows best.