I was named after my maternal grandmother, who died when I was still very young, so I don't remember much about her. I do remember that my mother loved her very much and that she'd be hurt if she thought that I didn't like my name or I'd changed it. But I'm happy with it and have kept it. It would be difficult to get used to a different one. If I'd been given a name like one of the weird ones given by some American parents, I might have thought differently.
Like many other people, I've changed my surname, and like many other people, I changed it back again. My sister changed her surname twice, the first time when she married and the second time when she divorced. She also changed her forename because after her divorce she wanted a whole new life. That's not entirely possible, unless you move away and abandon your old life and all the people in it. You might do it if you were in witness protection, of course.
According to gender identity lore, there are two cardinal sins. The first is misgendering someone, or referring to them using the pronouns appropriate for their sex, which is different from their gender, which is an assumed characteristic or affectation. The second is dead-naming someone, which means using the name they had before they decided to transition from one gender to another. It's considered worse then a faux pas to accidentally use the former name of someone who's done this, apparently.
We write our own life stories. My memory is rather moth-eaten, but others may remind me of things I've forgotten or something will pop up. Some memories may be shared when family and friends gather to mark my death, assuming they do. When your flesh and blood is gone, memories persist. If you've had children, others may recognise familiar characteristics in them.
We've no control over what other people remember about us. When we die they'll think of the parts of our lives that we shared with them, good or bad. So whatever you call yourself, the person behind the name will still be there. You can no more erase the part of your life you shared with other people than you can erase your essential existence as a woman or a man. Your name won't be dead, just unused, except by other people who might forget, or not know.
So, the moral of this post, and I'm sorry but there is one, is that trying to control other people's thoughts or memories is the stuff of Orwellian nightmares, and no one is likely to remember you kindly. Your epitaph may reflect this.