Praise be to Allaah.
There is nothing wrong with naming the bookstore after Shaykh
Ibn ‘Uthaymeen (may Allaah have mercy on him) or after anyone else who is
known for his knowledge, religious commitment, jihad and so on. There is no
reason why one should not do this, rather that is keeping their names alive
and reminding people of their virtue and good influence, so long as the name
is not that of one of people of innovations and deviance, etc., and so long
as the bookstore will not sell forbidden things that would reflect badly on
the name of the Shaykh (may Allaah have mercy on him).
This is something that people do. Bookstores have been named
after Ibn Taymiyah, Ibn al-Qayyim, al-Dhahabi and others, and no scholars
have objected to that.
And Allaah knows best.