Replays are strange in renpy. They reset all of your variables to default when you replay them, so MC's name becomes Manager. There's not much I can do about that, that I know of.
I'm still learning the ropes with renpy so take my info with a grain of salt, it's all trial and error for me and I haven't tested it yet but I see you have it set up so the players name isn't persistent?
python:
name = renpy.input ("What's your name?", "Manager")
name = name.strip()
If you set it up as a persistent, something like
label getPlayerName:
$ name = renpy.input("What is your name?", "Manager")
$ name = name.strip()
if name == "":
jump getPlayerName
$ tmpname = name
$ persistent.name = name
You should be able to add , scope={'name': persistent.player} to the replay buttons to have it remember the players chosen name. I assume you would have to set each characters name as a persistent like $ persistent.name = linoname but I don't know enough yet to say anything for certain, just something to hopefully point you in the right direction. I have been poking around the code of different games and that is just some stuff I have noticed.
Edit: It seems it may have to do more with persistent.player.
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