Optimal timing to change my last name

Lots of people publish under things that aren't their legal name (nicknames, middle name, one last name instead of two), and I've never heard of it being a problem for anyone. As for the timing, in all the cases I'm familiar with (and other fields may be different from math), there's a time after acceptance where you can make minor revisions and I think it shouldn't be a problem to modify the name you're using then.

I just went through a similar process last year. Before submitting our revision (this was my first publication), I contacted the editor and said that I was about to change my name and asked whether it would be accepted to simply change my last name in our manuscript. The editor gave me a green light and also contacted the journal's administrator, and that was that. For obvious reasons, editors are much happier that you do such changes before the actual publication takes place than come asking for it afterwards.