Davos number 1 lands in discard

Davos number 2 lands in hand

is that correct or does claim 2 require to specify 2 different characters?

From the entry on Military Claim in the Rules Reference Guide, p. 13:

"The same character cannot be chosen more than once to satisfy claim for a single [Military] challenge."

So you have to choose 2 different characters for a 2-claim military challenge, even if you can save the first one.

This should make sense since all targets for claim are chosen at the same time and a single effect cannot target a card more than once.