"MOBA" or multiplayer online battle arena was coined by the makers of LoL so that when asked to describe the game people would have something to say other than "it's like Dota." They wanted to dissociate their game from Dota, that's understandable, but the problem is that "multiplayer online battle arena" is a very poor name for the genre, as it's vague and doesn't really describe anything about the gameplay. It could be used just as easily to describe Battlefield, or really any other multiplayer PvP game. It also sounds dumb, but I suppose that is a matter of personal taste.
The most suggested alternative is "dotalike," named under the same convention as "roguelike," which denotes a game "like dota." I think this is more fitting, but is still a pretty loose description as it does not identify which aspects define the game, and it becomes less relevant as the genre branches out.
Surely the wonderful minds on this board can come with a better name for this genre of games. What are some of your ideas?
ARS - Abusive Relationship Simulators. You'll be verbally berated for everything and blamed for every mistake whether you made it or not, or even whether it was a mistake or not, then immediately begged not to leave.