No, it should still be called feminism. That’s what it is. It’s an ideology with a ton of different variants/branches, with the most ‘generic’ sort of definition, from dictionary.com, being the advocacy of women’s rights on the basis of the equality of the sexes. Feminism has always been about this, hence the advocacy in favour of equity in areas where women are under-represented, but no advocacy for non-women in areas where women are ‘ahead’. Sorta like how left leaning sorts point to a theory of equity that values the equality of outcomes to justify things like DEI – but if anyone points out that the aggregate ‘outcome’ from our healthcare approach results in women living ~5 years longer than men on average, meaning an ‘equality of outcomes’ approach should preference men’s health care needs until that gap is closed, suddenly they’ll have excuses why their vision of equity exempts that particular case.

There’s no real reason to change the term feminism, it fits with what feminist ideals generally are and has a valid place as a general ideology. It’s especially pertinent in areas where women’s rights are massively under-represented / ignored.

Equality of all people is egalitarianism. It’s been around for longer than feminism, in general. Feminists are not egalitarian, as they aren’t about equality of all people, and instead only focus on a specific niche, and ultimately are ok if their niche is preferenced / comes out on top. Both ideologies can exist just fine. What needs to change is your perspective of what feminism is, as you seem to mistakenly think its about equality for everyone.