Watley
Watley could refer to:

 Watley (Lieutenant), a crewmember who served aboard the USS Enterprise
 Watley (Julian Bashir's great-grandmother), Julian Bashir's great-grandmother

You may also be looking for the similarly spelled:

 Whatley, a crewmember who served on Deep Space 9
 Charlie Whatley, a Starfleet Admiral
 Kevin Whatley, the son of Admiral Whatley