Hmmm, I thought I had come across this name before as a variant form of Gyða and Guðfríðr (see
Gytha), but when I just looked her up, there is only Gyta and
Gytha.
I have to say I'm secretly fascinated by Gyða in a very GP sort of way. Gytta, however... I don't know, this variant (if it is one in the first place) is just not for me.