The name seems to be simply : DotA (Defense of the Ancients) since this is this mod who made this genre popular.
Wikipedia states that:
Terms commonly used to refer to the Dota genre include but are not limited to "AoS style games" (Note "Aeon of Strife" a mod in StarCraft), "DotA style games", "DotA based games", "Dota games", "DotA clones", "DotA-Likes", "Action Real-time strategy games", and "Action RTS games". Dota games can also be simply referred to as DOTAs. Riot Games has also been known to use the self-coined term, "Multiplayer Online Battle Arena".
MOBA terms seem not widely used and, for the records, is currently redirected to DotA genre on wikipedia.
I think a common agreement is not defined. And in my opinion, this is gonna end speaking of those games as "Dota-likes" as it was for Doom and its "Doom-likes".