No, Pena and Peña are not the same last name, though I agree with Ellen that the tilde could have gone missing in emigration.
There were a lot of problem with the ñ (typewriters no designed specifically for Spanish-talking countries did not have it) in international paperwork. In recent days, with the arise of the WWW, early systems and keyboards did not support it. Even today, website domains do not accept ñ as a valid character.
On the other hand, last name Pena could also come from the Italian last name Penna (with an n missing), which has the same Latin roots as Peña (rock).
If you have trouble adding special Spanish characters you can try these easy shortcuts to the basic ASCII code:
ñ= alt+164
Ñ= alt+165
á= alt+160
é= alt+130
í= alt+161
ó= alt+162
ú=alt+163
(It's not necessary to use tilde in capital letters, except the Ñ, but there're very few words that start with ñ)