My experience with name change.
I had to change my name once because the Judge clerk (I was granted asylum by Immigration Judge) misspelled my last name and put an extra “R”.
I had 2 RTDs with the wrong last name and 1 Employment Authorization Card, plus many plane tickets. BEFORE I filed I-485 I sent a letter to the clerk here downtown L.A. and she was very nice, she retrieved all my files from the Laguna Niguel, CA INS offices, edited an “amended order” had the judge sign it and sent it to me.
I attached a copy of both orders to my I-485, as well as my new I-131s, and now my life is back to normal. Hadn’t I done it at the time I filed for residence, I would have to wait ‘till citizenship to avoid complications. I think it depends on the circumstances of your name change (maybe you just got married, no big deal) - but my case was a misspelling and I was basically living a double life having to be careful where and how I wrote my name.
I hope this helps.