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Frieda works, esp. as it would be less likely to be mis-pronounced than Frida... Frieda is quite sensible on its own and doesn't have to be a nickname for something. I would never assume someone named Frieda was using a shortened form of her name, though I realize that in some cases, it's possible she could be.
Possible middle names (not a complete list, but some that just came to mind):
Joy
Leanne
Charisse
Brittany
Louise
Janelle
Karen
Nancy
Joanne
Staci
Stacey