A brother said to me that it is not permissible to do this. Is that correct? Should I change this name?.
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.