Senators is a boring name. I don't want to think about politics while trying to enjoy a game. It sounds like New York Stock Brokers or LA Producers. Accurate, but just not fun. Nationals is relevant enough.
Not a big deal, to be sure but ... what exactly does "Nationals" mean? We are hardly "America's team" in baseball. And, yes, we're in the National League but that really has no connection. So are 14 other teams.
Maybe the team should've gone for neither Senators nor Nationals. I've forgotten what the other names put forth were. Must've been pretty bad.