Hanuman is not same word as Monkey. Calling Hanuman Monkey is derogatory. So you can call your God as Hanuman, Shiva, Bhrama. Or you can also call your God as Jesus, Bhagwan, Guru.
I promise you 1000000%, there would be no ban by any court.
Its about equality, so if you want to name you pet as Hanuman. then do you accept if we name our pet as Allah?
Rule is simple accept one of below options (all based on equal rights for all irrespective of religion):
a) whatever applies to you, applies to others as well. If you use other God's name for pets, others can use your Gods name as pets.
b) If other's use Allah for their God's, you can use their God.s name for your God.
c) accept both b and c
though I am personally not in favour of using Allah for God by other religions. but if some people/religion want to use it then there is nothing for a court to ban it, because Its not wrong or immoral or unethical.