You could, but you don't have to. People name their Stands a lot of things. I mean, hell, you could name it "Purple Rain" if you wanted to.

[He picks up his towel and gives his hair another rub, just for good measure, then wraps it around his waist and finger-combs his messy curls back out of his eyes.]

It's yours. You pick what feels right to you. Or, you give it to somebody else and you just go with what they say.