Is it just me, or does anyone else find his refusal to tell you his name really bizarre?
When I read the OP, it did send up a few red flags in my brain. But the more I thought about it, the more I realized that it really depends on the situation and how he was playing it. I'm not sure I would withhold my name as it seems risky, but the OP doesn't seem worried, so he must know his own game.
I agree that it's all in the context. We don't know that he "refused" to give his name, since that hasn't been stated. Yes, it would be weird if OP asked for it and he didn't give it. But it could be one of those things where she got home and realized she'd never asked and he'd never thought to mention it.
Also, I agree with "old fashioned" SleepyKitty
I don't think texting is a good way to communicate once you've actually met the person. There's just too much nuance, etc. that gets missed and it impedes real communication. So I agree there's no problem with OP being the first to communicate, but it should be a phone call.
And of course updates are requested!