Rizu in A Profile. At one point Masayuki is worried for her when she uses the more standard "atashi" to refer to herself.
Katawa Shoujo's Misha plays with this trope a lot. She sometimes uses what sounds like third person speech, but it's because she's voicing Shizune's signs. She also inverts the trope by speaking in first person for a third person. Lastly, she's not above lampshading it either, which is justified when it's to make clear who's actually speaking.
Da Capo's Miharu refers to herself in third person.
Oko San, from Hatoful Boyfriend, only ever refers to himself as "Okosan". Since he only speaks in subtitled cooing, there's a difference in how the heroine translates for him (pretentious and Hot-Blooded, using the "grandiose" third-person) and how the other birds translate for him (birdbrained and childish, using the "immature" third-person).