I'm going to assume this code is in your script for entering the character's name during the game...
first try it like this
$ mcname = renpy.input("What is your name?", default="Daniel").strip() or "Daniel"
$ persistent.name = mcname
then in your code at the labels for the replay do this
label replayLabelHowOriginal:
if _in_replay:
show screen Replayexit #the optional exit provided with the gallery
$ mcname = persistent.name #see what I did there...
that should fix your problem