Question Summary:
Is it permissible to give a cat a Muslim name?

Question Detail:

Is it permissible to give a cat a Muslim Arabic name?

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
It is permissible to give a cat a name in the Arabic language[1]. If by Arabic name in your query you mean Muslim names, then the name should not lead to disrespect to any Muslim name, for example naming the cat after the names of Prophets (Alayhimus Salam) and Sahaba (Radiallahu Anhu) etc.
 
 And Allah Ta’āla Knows Best
Ismail Dawoodjee
Student Darul Iftaa
Zambia
Checked and Approved by,
Mufti Ebrahim Desai.
www.daruliftaa.net