First off, welcome to Pigeon-Talk, and congrats on your new pets
To help tame them, when it's time to feed them, try offering it in your hand first before putting it in the dish. Handfeeding is a good way to earn their trust. But of course if they're full of food already, won't do much good.
I would not let Ultima out, because there is a risk of her going back. It sounds like she's an adult bird (although we can't be sure without pictures), so she'd probably leave. Her companion could be let out after a month probably.
From what you've said, can't say for sure who is what gender-wise. Both males and females can be calm or aggressive. Dominant birds like taking over the highest perch and nest box. But, it does sound like the nameless bird could very well be a male. When 'he' bobs his head, does he puff out his neck or coo?
The first name for Ultima's friend that came to mind, was Max. Could be a boy's or a girl's name (like the girl in the book Maximum Ride).
It's much too late to band them now with anything permanent. Seamless bands can be traced to the owner and have unique band sequences. But, those have to be put on the legs while they are still in the nest, so that they grow into them and can't be pulled off. However, there are snap-on and spiral bands you can put on them. Although since you only have two pigeons, it probably doesn't matter much.
Your setup sounds good to me. What kind of perch do you have in there? As long as they both have somewhere to sit, it's fine.
The easiest way to clean is to get a cheap scraper if you don't already have one, and just scrape out the droppings every day. They'll get used to it quickly, and it shouldn't take but a minute with only two birds