In 5e, does the Hydra regenerate 20 HP or 10 HP? It says per head regenerated, so does that mean per stump regenerated on or per new head?
It gets 10 HP per head regrown
From the Hydra in the MM pg. 190, emphasis mine:
Whenever the hydra takes 25 or more damage in a single turn, one of its heads dies. If all its heads die, the hydra dies.
At the end of its turn, it grows two heads for each of its heads that died since its last turn, unless it has taken fire damage since its last turn. The hydra regains 10 hit points for each head regrown in this way.
The key word there is each. So, if at the end of it's turn, 3 heads have died but there is still 1 alive, the Hydra will grow 6 new heads, gaining 10 HP per head grown, for a total of 60 HP. The heads already alive do not regenerate HP.
The HP regeneration is per head regrown.
20 hp, if it lost one head
The hp gain is per head regrown not per head lost. The hydra 'regrows' 2 heads for each head it loses, so it gets 20 hp, effectively, for each head that was severed.
It isn't going to always be 20 hp, though, because the hydra might lose more than one head in a single round.