I'm surprised everyone's forgetting vim already has a proto-multicursor mode.
Go into Visual Block mode (Ctrl-V) select all the lines then it's just A<delete ,>: Enum.Name0,
After that you can just select it again in visual mode and g Ctrl-A to get the right numbers.
If anything the g Ctrl-A part makes Vim way better than most multicursor editors.
g Ctrl-A increments all the numbers, but every instance gets incremented by one than the previous.
First line would be Enum1, second Enum2, third Enum3. It's a really neat feature imo.
Though I did make a mistake, if you selected everything it'd catch the name numbers too, so you'd have to go into visual block mode and only select the enum parts, then do g Ctrl-A.
That said the numbers probably weren't supposed to be taken seriously now that I think about it.
After that you can just select it again in visual mode and g Ctrl-A to get the right numbers.
If anything the g Ctrl-A part makes Vim way better than most multicursor editors.