I thought the name Mario Mario was first brought up in an old Nintendo Power. I forget who came up with it, it may have been some writer there, but I think it may even have been Miyamoto himself.
If I may... you can visit
www.mariomonsters.com to learn what games Mario enemies appear in. It's definitely not my own site.

To be more specific, though, here are Super Mario Bros. 2 enemies' first appearances in the Mushroom World:
Super Mario Bros 3: Bob-omb
Super Mario World: Pokey and Ninji
SMW2: Yoshi's Island: Shy Guy and Snifit
SMRPG: Beezo (listed as Shy Away) and Birdo
Also, Wart had a cameo as "Mamu" in TLOZ: Link's Awakening.