Is there an approval process that I must follow in order to move the “Google” that is in the left-hand corner to another area of the map? I have an application where my UI will cover these words and would like to display them in another location on the Google map. I know how to do this in iOS, just don’t know if there are legal concerns with Google in doing so.

You can’t.. That violates a Google Maps term:
and the App Store Review Guidelines: