Yep, I've named my electrics, though not my acoustics. Most names are based on color or model name, and all have some sort of logic behind them, though in some cases that logic is attenuated at best.
Here they are with their names, see how many you can figure out why they have the names they do! (Note: while many are obvious, figuring out at least a couple of the others is unpossible without "insider information.")
Left Column / Right Column:
Daisy / Dani
Farrah / Goldie
Stormy / Corinne
Joan / Sonia
Seven / Candy
Violet / Ol' Blue
Honey / Theresa
Chrissie / Natalie
Birdie / Brownie
Ruby / Raquel
Cherie / Rickie
Nell / Blondie
And no, when you have 3 Telecasters, you can't just call them "the Telecaster." It's actually more efficient to say "Brownie" than "the Tex-Mex Tele Special," or even "the brown Tele."
But I don't do it for efficiency's sake. It's fun. When my kids were little they especially got a big kick out of it. Not that I don't.
And yes of course guitars are of the feminine gender. "C'est la guitarre, n'est-ce pas?"