I have a cousin called
Melissa. She was born in the 80s and I've never come across anyone else with the name. She doesn't use any nn though.
I don't think
Melissa is dated at all. It's really sweet and feminine sounding and would be perfect for a child today. I know it was really common in the 70s but I don't think of it as a fad name at all. A good nn would be
Lissa or Lissy,
Missy is okay, but definately NOT
Mel or Mellie.
I don't like
Melisa though. I prefer
Elisa.