Phoebe is a beautiful, timeless name!
OP, I will offer you a different perspective. My parents changed my name because they changed their mind when I was one. I don't remember the original name being my name, but it's still a massive headache sometimes.
This is what happened (with fake names). My name at birth was Lucy Catherine. My parents decided to shorten Catherine to Katie and called me Katie. To all intents and purposes, that was my name. They registered me at school as Katie, doctors as Katie etc, but Lucy was on my birth certificate.
At 17, I applied to uni and UCAS flag that my name is Lucy but my GCSEs are Katie. Take loads of phone calls and a solicitor letter to persuade them that both are me.
My parents are like, oh shit, we better change her name by deed poll. We do that, but not before my national insurance number is issued as Lucy.
I have told HMRC several times but it never gets updated and they still think I'm Lucy. I'm 36 now and recently started a new job and it messed up my tax because work said they didn't employ a Lucy XXX. It was a massive pain to sort out.
There have been other things over the years.
So I guess what I'm saying primarily is you have chosen a beautiful name and it doesn't need changing. BUT if you do change it, please get your admin in order and change by deed pool straight away so as not to cause your DD trouble in future!