'Spelled' is the only correct word in American English. 'Spelt' is an alternative that is quite common in British English (there are other verbs which function the same way e.g. burned vs burnt). 'Spelled' is of course still correct in BrE. Both are correct for the second one.

Theoretically it is - wrongly | incorrectly as you're using an adverb. Practically - everybody would be saying - you spelled my name wrong. Were you to be as correct as possible - "You have spelled my name incorrectly."