I like/can tolerate:
Bizzy
Tessie - much prefer
Tessa or even
Tess though
EssieBillieDillie
GeorgieMellie
Trixie
I dislike
Effie,
Hattie, Dovie & Birdie. I don't think those should be given to a child as nicknames, and definitely not as stand alone first names!
If I had to use one for a daughter, today it would be
Billie, nn for
Sibyl (not
Wilhelmina!).