Looking for advice

Hi! I am fostering a pigeon right now . She's got a huge cage with grit, food, water, plushies and toys, and I've got treats.

I'm not sure how to get her comfortable with me, or how to get her to learn her name. Often why I try to hold her, she flies and perches somewhere (well, not really, she chooses the most unstable spots)

How do I help her feel more comfortable? I like to put her halfway under my blanket and rest with her. I usually pull it away gradually so she can leave if she wants. Unless I startle or move too much, she stays in place. She does these slow blinks. I try to slow blink at her aswell.

I try to bob my head but it seems to scare her.

Oh, and the other day she kept flying off, so I tried the blanket thing and she ended up burrowing into it and making this weird clicking noise, not the usual coo. Is that bad? I assume so. I don't know how to help her. I mostly work with wild birds.