A better argument is that the president doesn’t determine the common, accepted name of bodies of water in English. Even American English. And especially ones outside US borders.
Be that as it may, from the mexico lawsuit stand point, is there any rule of law being violated by refering to something by the wrong name? It doesn't really matter if the president lacks the authority to change the de jure name or what the de facto name is, if google has no obligation to use the correct names for things.
I do also, separately, think the lawsuit seems odd. But I guess when confronted with absurdity… file absurd lawsuits? I dunno, speaking of maps, we’re in the part that reads “here be dragons”.
The name’s the same as it was.