Changing Legal Name and Updating Website for Trans Artist

Hi everyone, I'm a trans artist in the middle of changing my legal name completely and was wondering how that would affect my SEO for my website. I'm a writer and artist and have a following under my current name. If people will still continue to google my old name, is there any way to still direct traffic to my current site (which I'm also updating to match my new name)? Basically, is there a way for me to edit my site so that both my old name and my new name direct folks here when they search me? Thank you!