How do I handle people rejecting my new identity?

I’m planning to change my name to reflect the person I truly am and to protect myself from my narcissistic mom. My birth name feels like the old me and my new name will be the new me. I’m worried some people might see this as strange or even creepy. I am changing just my name nothing else. How can I stay grounded in my new identity for myself, not for acceptance or validation from others, when people react negatively?