Is there a name for this drink?

Vodka, sweet vermouth, dash of bitters.

Maraschino cherry optional.

I haven’t tried it with gin.

Replace the vodka with whiskey and you’ve got yourself a manhattan. Call it a vodka manhattan, I guess.

with Gin, it’s an Artillery

I couldn’t find it with vodka on that site

This looks like a variation of a Dean Martini, though those are usually served with an orange wheel.

Drink up.