I already asked this but didn’t get much of a response, so I’ll try again. Any takers?
I think that [name]Sophia[/name] or [name]Sophie[/name] would make more sense if you’d like to call your daughter [name]Sophie[/name], but if you chose to name her [name]Josephine[/name] and call her [name]Sophie[/name], I don’t think there’d be any harm.
Good luck! 
Another option would be Sophina as a nn. I found that unusual name aways back in my family tree and I [name]LOVe[/name] it
I think you could easily get [name]Sophie[/name] out of [name]Josephine[/name], I mean all the letters are there right? Actually, the more I think about it, the more obvious and plausible it seems! If you can get [name]Hank[/name] out of [name]Henry[/name] and [name]Dick[/name] out of [name]Richard[/name] then you can definitely get [name]Sophie[/name] out of [name]Josephine[/name]. What a good idea! I admire your creativity:)
Hey I love the name [name]Sophie[/name] , think you could definitely use it as a nn for [name]Josephine[/name], that or Sephie, [name]Fifi[/name], or [name]Effie[/name]
I don’t really see [name]Sophie[/name] as having a natual connection to [name]Josephine[/name], but if it works for you, then go for it.
Btw, I’m curious… What sort of nickname would you use for Mnemosyne?
– [name]Nephele[/name]
[name]How[/name] about Mne Mne?
I think it would work.
[name]Mo[/name] 
Meme ([name]Mimi[/name])
I think it works because the sound is there but I don’t know why you’d use another actual, unrelated name as a nickname. I think it would be a little confusing - what would you introduce her as, how would you label her things, etc. If you introduced her as [name]Josephine[/name] and then called her [name]Sophie[/name] would people get confused? I don’t see the same problem if you introduce her as [name]Josephine[/name] and call her [name]Josie[/name] or [name]Fifi[/name] or [name]Sunshine[/name] or [name]Honey[/name] or whatever.
Thanks for all the responses! [name]Just[/name] to clarify, I’m not actually expecting…just thinking.
As for a Mnemosyne nickname…I’ve been wondering that myself! Here’s what I’ve come up with (I wouldn’t really use any…well, maybe [name]Minnie[/name]…and I like [name]Nina[/name]/[name]Nena[/name] but think it’s unlikely):
[name]Nemo[/name] (Mnemo?)
[name]Mossie[/name]
Mouse
[name]Monnie[/name]
[name]Ossie[/name]
[name]Minnie[/name]
[name]Nina[/name]/[name]Nena[/name]