I got this from translating 'G-d is my G-d' on Google Translate. However I don't know how to pronounce the Hebrew. Can somebody give me the pronunciation on this and is there a Hebrew name that means the same thing.
It is pronounced elohim hu elohim sheli, but it sounds strange and tautological in Hebrew. There are Hebrew names that mean approximately the same thing, like Yoel (Joel in English) and Eliyahu (Elijah). Yoel literally means "Ya [a divine name] is El [a divine name]", while eliyahu might be translated "Yahu [a divine name] is my god".
Perhaps what you are looking for is something like what Moses tells the Israelites in Deuteronomy 4:39, that "adonai hu ha'elohim": "The LORD [the divine, four-lettered name] is God."
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Pronunciation transcribed using letters in another alphabet is always ambiguous. The existing (good) answer, by Shimon bM, writes elohim hu elohim sheli, but, then, you don't know whether that initial e is pronounced as in e-mail or as in end or as in fiance. The right way to transcribe pronunciation is using a phonetic alphabet, either the International Phonetic Alphabet or some other; the IPA is the most 'official' standard. Even using such a phonetic alphabet, there's still ambiguity, because every symbol represents a range of sounds, but the ambiguity is far less.
So here goes (in IPA).
In a modern Israeli accent, אלוהים הוא אלוהים שלי (actually, properly, אלהים הוא אלהים שלי), is /ɛloˈhim ˈhu ɛloˈhim ʃɛˈliː/. (Modern Israeli Hebrew doesn't really have distinct /e/ and /ɛ/, so what I transcribed as /ɛ/ others might transcribe as /e/.)
In my own (Americanized Ashkenazi) accent, it's /ɛlowˈhɪm ˈhuw ɛlowˈhɪm ʃɛˈlij/.
Some might say /ɛlojˈhɪm ˈhiː ɛlojˈhɪm ʃɛˈliː/.