I'd respond that creating synonyms does not a new entity make - it just gives a new name to an existing entity.
At that point the choice of name for the same thing is arbitrary.
If I choose to create a language to describe the word that matches a strong atheist's in every way except that I use theistic names in place of atheistic names and I choose one over the other I am expressing a linguistic preference - I am not describing a different universe.
I agree, and I have argued as much many times. But it still means that what you are stating is that there is no god for any definition of "god" that I will accept. Now from the point of communication, that is all well and good. Words must have meanings. They cannot be made up ad-hoc. Or more correctly, they
should not, but theists will persist in doing so. What can you do about that? Nothing really. It would be wonderful if you could get them to agree to a general definition of what a god is before you attempt to engage them in any discussion, but that is simply not going to happen. Essentially, their definition is circular.
Theist: I believe in God.
Me: What is God?
Theist: It is what I believe in.
As such, you could say that they are not even talking about God, but rather their beliefs. Occasionally you'll even hear someone say something like "I believe what I believe", as if that somehow made it clearer.
So ultimately, I agree with Piggy and most others here that the theist position is fundamentally illogical and... er... unlexicographal. Yet opposing it still amounts to saying, "That is not a definition of god," and we simply cannot demand that people surrender the right to define god as they choose, regardless of how many dictionaries and theological texts they defy.