Yes, you can legitimately buy Bitcoin from CoinBase with your real details. I doubt they would allow you to go ahead with the order if you used false details anyway as you would trigger their fraud detector. Yeah, about the tumbler sometimes it gets a little overwhelmed with users and they just changed servers today I believe so they have a few teething problems to deal with. Give them a day or two, good luck OP make sure to stay safe and never become too relaxed when purchasing always stay 100% on the ball when it comes with security!