Most streamers I watch don't give their builds any special names, it's just profession/elite + build, eg. "Firebrand build".
Personally I love thinking up names for things. It's not like it's necessary to give your builds unique names, but I find it fun to do so and it instantly helps me to remember what build is what. The way I come up with names for mine is by combining names of two traits that I'm using in the build. The traits themselves don't need to have any significance.
Some examples of my build names;
How about you guys? Does anyone else give their builds special names? And if so, how do you think up the names?
Necromancer / Engineer | Maguuma | Diamond Legend
[YWY] Weeping Valley //
My Youtube: Shroud