Refreeze ground hamburger as hamburgers after thawing?
Never re-freeze raw meat. I have run 2 commercial food establishments and had to be qualified in food safety so this is what I know...

The freezing process arrests any of the bacteria in the meat from causing putrefaction but as soon as the meat defrosts these bacteria start their work again at an accelerated rate, re-freezing will cause a repeat action and food poisoning will ensue. And ground or minced meat usually has a higher bacteria level due to the extra handling, increased actual surface area due to many smaller bits and the fact that those tiny pieces warm quicker. 

If you want to freeze individual hamburgers, make them up as soon as you get the mince and freeze what you don't want to use straight away.

I hope this helps