Abandoned black cat is a girl

This morning, when I got up to let the dogs out for a wee, I spotted the black cat who was abandoned here last Tuesday under my car.  I was so relieved. There was no sign of her at all yesterday at either morning or evening feeding times so it was really good to see her, the weather is soooo cold.  I thought the dogs might have chased her and she was too frightened to come back, especially after all she's been through - dumped here sometime last Tuesday when no one was home in the freezing cold weather (some nights - 7 degrees!) with no warning, no call, no note, nothing.  If I hadn't gone into the blue shed and seen the unfamiliar dustbin lying on its side, an unfamiliar towel in it, the lid hanging off,  I'd never have known.  The cat obviously had got out of the dustbin and scarpered through the permanently opened cat flap. There was no sign of her for two days until I heard her meow in the distance on Christmas Eve and suddenly she appeared, a lovely black young cat with a round face and yellow eyes. She's been coming at feeding time every day since except yesterday for some reason. 

Then later this morning she actually came into the utility room while I was getting the food ready for all the cats and I was able to pet her and give her a cuddle and discover she is a girl. She is an absolute dote, very friendly, purring and meowing happily and in great condition. She seems to be standing her ground with all the other cats.  No mean feat!  Whatever her story is, I'll probably never know. Wonder if she's spayed?  And what shall I call her?