For all intents and purposes, there are only 2 references to Grover that can be found online. The first is regarding the 22nd & 24th President of the United States of America, Grover Cleveland (bet you didn’t know he was the only President to serve non-consecutive terms, huh?). But his real name was Stephen.
The only other Grover that seems to have existed with any success was the restless blue monster of Sesame Street fame.
9 times out of ten, people will think of the latter when the name Grover is mentioned. Do you REALLY want this for your child?