Whovian is a fandom name, a moniker which members of the Doctor Who community adopt when they have absolutely no dignity or self respect whatsoever (but then again, since they enjoy Doctor Who, could they have even had any to begin?). Usually used by Tumblr members and YouTube vloggers with only 4 or 5 subscribers.
People who use the term tend to be more obsessive about the show, frequently using terminology spoken by the characters (Timey-Wimey, SQUEEE, etc) and lacking any sense of humour whatsoever. They'll commonly source out "You know you're a Whovian when..." lists, which usually feature cliche points like "You DON'T BLINK when you see a statue!", to which they'll react with "ZOOOOOOOOOMG SO TRUE THIS IS SOOOOOO ME xDDDDDDDD". Sometimes they'll even do fanfiction which crosses over with other franchises like Sherlock or Star Trek.
If you meet a fan who uses the term Whovian, AVOID THEM.