There aren't that many but:
Rach, Rachy, Rae,rayray or you could stick with Rachel
I get called brat from my sisters!! but that could just be me!
Rachel Diaz goes by Rachel Days.
Rachel Margolin goes by Rae.
Rachel London goes by London.
Rachel Longmore goes by Rach.
Rachel Skarsten goes by Rachie.
Rachel Rutz goes by Rutzy.
Rachel Sandlin goes by Sandy.
Rachel Utzig goes by Rach.
Rachel Arlook goes by Rach.
Rachel Kahan goes by Mcskate.
Rachel Huggett goes by Didi.
Rachel Desmarest goes by Desmarest.