If one must eat on yom kipper, does he make any day-specific additions during benching?
Taz (Orach Chaim 618:10) and Magen Avraham (618:10) cite variant opinions as to whether Yaaleh Veyavo needs to be recited (and also Retzeh, if Yom Kippur falls on Shabbos). According to the Taz neither one should be said, while according to Magen Avraham it is better to add them.
Pri Megadim (Eshel Avraham 618:10) adds that in any case, if one did omit them, he should not recite the makeup berachah "Asher nasan...," since it might be a blessing in vain.
Rav David Yosef (the son of Rav Ovadia Yosef) rules (Otzerot Yossef 14:19) that one should add Ya'aleh v'Yavo, and identify the holiday as ביום הכיפורים הזה, ביום סליחת העון הזה.
The Shulchan Aruch (OC 618:10) rules like the Rosh (quoted in the Tur) and the Rambam (quoted in a responsum of his in the Beit Yosef) that one who ate permissibly enough to be obligated in an after blessing should mention the holiday in Yaaleh veYavo. Although the Taz there (sk 10) argues, the Mishna Berura (sk 29) leans toward saying it (as well as Retzei if Yom Kippur falls on Shabbat). Interestingly enough, the Aruch haShulchan (:17) quotes the argument and concludes by noting that he doesn't know what the common practice is.
For a characteristically thorough survey of the sources see Rav Ovadiah Yosef's responsum in Yechavveh Daat 1:44 where he concludes unsurprisingly in accordance with the Shulchan Aruch that one would say Yaaleh veYavo.
You should add "Yaaleh Yeyavo"