People are rarely asked for marriage certificates, but they CAN ask for them. And by gosh they should! You've got a BC in the name of Mary Smith and now a DL in the name of Mary Jones? Seriously? They should absolutely ask you for the legal document showing that you went from Smith to Jones.
If I had changed my name I would bring it and show it every time. (except that I don't go outside of the country without my passport)
If DH changes his name to mine after his mom passes (he has wanted to change it since we got married but the crud would have hit the fan if he had while his parents were around), don't you want HIM to have to show the legal document bridging the identities? You can bet they would require it from any man. So they should require it from women.
I'd bring it. And show it.