I've heard the mazuri brand is a good lab block..so she should be getting the fibre she needs from there, so I wouldn't worry too much about her skipping out the alfalfa pellets (my little boy emptied everything out of his bowl..except the alfalfa pellets!)
You seem to be doing a good job at making her happy
One of my hamsters seems to stay in her house a lot, and just wander around/tunnel around occasionally, so it could be that she's awake..but just staying in bed, also..my girl runs into her house as soon as you turn on the light, so it could be that yours is doing that even..
As for names..I'm awful.. but sunshine is cute, or you could try something food related such as cupcake, or mocha
I hope she continues to recover from her illness, and good on you for spotting it..now I'll let somebody who is more experienced help
