Ditto. Don't go thinking that it's anything like a written-off car. If it's airworthy it's airworthy.
Regarding getting it registered - has it been de-registered?
Posts crossed...
The aircraft registration doesn't change (unless you want a new one, but why?).
The damage gets repaired, the aircraft gets inspected and signed-off as airworthy. If the C of A hasn't run out you go flying again, so long as you have insurance in place.