Sheema is more Persian actually (nitpicking about origins, hooray). The Indian name is actually Seema, but then again, India is pretty varied with naming. I've never met a Sheema myself though.
Also, while Shiva is in fact Indian, the name is pronounced as Shiv. The main reason this is the case is because when a Devnagari language is written, the final sound is written as a whole letter (the script allows for half and whole sounds), despite not being pronounced as such. It's also a very, very masculine name, so if someone is actually trying to name Sheema that, then I am slightly troubled. Seriously, it's so masculine that Hindus worship the dude's dong.