No that’s the point it would not be in defiance of the government because the government don’t have the authority to tell private companies or individuals what bits of water should be called. All president has the authority to do is dictate what federal agencies call it.
The whole reason that everyone thinks this is a massive waste of time is precisely because he doesn’t actually have the authority to force anybody to do anything. 20 years from now I highly doubt anyone is still going to be calling it the Gulf Of America, it’s just a PR stunt to keep his supporters happy.
Why does it get its mapping data from? Because we don’t want an Apple map situation when they reckon the Eiffel tower is in the middle of the North sea.