While I can't find the reference to the other name, Uehara Tomomi is one of the aliases of Mami's VA, Kaori Mizuhashi. She's credited with that name as the voice of Haruka Suzumiya from Kimi ga Nozomu Eien, an eroge.
The implication is that Kyouko wants Mami to do those voices in eroge.
The even bigger implication is that Mami's VA basically did porn voice acting.
Though the obvious one is that the artist did not do the research. Mizuhashi Kaori has done lots of voices, albeit highly inappropriate ones. I mean, some of her credits are shota/bishie (Yuuno from Nanoha and Laharl from Disgaea), non-speaking roles (Len and White Len), animals (yes, she has a credit for freakin' ARIA), and flat-chested girls (Martina Crespi from Strike Witches, Zefiris from Scrapped Princess).
Or it could be that the artist DID do the research and is using the fact that Mizuhashi Kaori HAS done porn roles as the joke.
Fun Fact: She was also Navi in the Japanese release of Ocarina of Time.
The title of the 4koma does seem to suggest the artist did their homework (as you said, Mizuhashi Kaori has done lots of voices -- hence, "Woman of a thousand names" as the 4koma title) . . . and is just having Kyouko be a pervert about which ones she's suggesting for the sake of the joke.
Updated
Woman of a thousand namesI can't do anything like that...Wh-...what are you talking about?You're all so good at imitating, I'm so envious!Uuuh? Try something, Mami-san!Aren't there lots of imitations just made for Mami-san?Like the imitation of Uehara Tomomi's or Amanami Nene's voices!smash!!Great gold leg!!