I never thought of myself as my birth name, so changing for me has been mostly easy...except for those times I still have to acknowledge my dead name. I'm only six days past my legal name change, so I'll still be dealing with the old name for a while until I get all my stuff sorted out.
It's probably different for someone who internalized their birth name - which I'd guess is just about everyone.
If I had had a unisex name or one easy to switch, I likely would have kept it, but done something to make feel more masculine. I also likely would have transitioned sooner. My parents had considered naming me Stephanie. If they had, I would have started going by Steve around 13 or 14. Could have given me 22 years of my life to live instead of just existing and plodding through, but no...they went hyper-feminine with the name instead.
If your old name doesn't make you dysphoric or otherwise cause you grief, keeping it would help minimize paperwork and frustration, IMHO. But if you want a new name, find the right one and go for it.
James