The Shulchan Aruch (OC 119:1) rules that one may add to a middle Brachah (i.e. from Atah Chonein to Shema Koleinu, inclusive) of Shemoneh Esrei a personal request on the topic; for instance, if one wishes to daven for a sick person, he may include it at the end of Refa’einu. In Shema Koleinu, one may add any requests he has. The Rema holds that one may only add to the end of a Bracha. The Shulchan Aruch quotes Rabbeinu Yonah that one who davens for many people should phrase his request in the plural, and one who davens for an individual should phrase his request in the singular, though if one adds to Shema Koleinu or the end of Shemoneh Esrei, he can phrase it however he wishes.
Other than those brief statements there (which is all the Shulchan Aruch quotes on the topic), how should one phrase it? If one is davening in Hebrew, should he add his requests in Hebrew as well? If one is davening for himself, should he just refer to himself in the first person, or should he use his full name (ben/bas mother’s name)? Does it even matter?