If you change your name to something neutral I think normal people will just take it for what it is. A name change. People who are into the trans ideology stuff will definitely think you are a trans man in denial who is making baby steps towards transitioning, but they don't matter. I'm sure they already think of you as trans-in-denial since you are a butch lesbian so there's nothing to lose there 😁

I changed my name by deed poll when I was younger for a different reason. My family thought a name that looks less "ethnic" on paper would appeal more to future employers. The process itself is quite simple and relatively cheap, but the aftermath might be disappointing. People I've grown up with still refer to me by my birth-name to this day, but that's on me. I never bothered to correct them because I didn't hate my birth-name.

You can introduce yourself to new people with the new name, but people who knew you previously may take a while to adjust. My family and friends used my new name a lot in the beginning but got lazy or forgetful and reverted back to the old one after the novelty wore off. Be very persistent in correcting/ignoring them when they use your old name. You might feel like you're being annoying or petty when you do it, but if you're serious about this, it's the only way they will get into the habit.