I mean, we do, but a surprising amount of people don't. This is precisely why the name should evolve. Well, that and the perspective that the movement's goals have changed significantly enough from individual liberation of women to comprehensive equality of everyone, which should come with a corresponding change in the name. These are related.
You are for all of it but the name, so you won’t support it?
It's more that if people are informally introduced to the movement, their preconceptions are formed by its name. This can turn them off from seeking or accepting the real nature of the movement once it's explained to them. As a reminder, most people put very little thought into this sort of thing, so making a good impression for the people who are potential allies is important. You can argue that that's stupid and shouldn't be necessary, but it won't stop it from working like that.
And don’t do what dummy above said and claim you support it but don’t use the label because it is gendered.
I don't think I've ever encountered a situation where it's useful to directly say "I am a feminist" because it's generally clear from my other opinions, but I would if the situation required it. I do agree that an alternative label would be better, though.