Hmm I would think it depends on the documentation involved with your name being legally changed.
After all, if you change it legally, what do you get to show anyone that matters 'see, this is what it was and this is what it is'.
At that point I would just show them the original document, prove you own the name, even if it is now legally another one and move on.
Only downside, well how often will you want to be telling people 'yes I was born different, what of it?'.
If it's a hassle and if the certificates involve enough gainful employ to be worth mention, then consider it a monthly cost and just do them progressively.