The Shach (Rav Shabtai Ha’kohen, 1621-1662), in discussing the laws of respecting Torah scholars (Yoreh De’a 242), writes that it is forbidden to address one’s Rabbi by his first name in his presence even if he adds a title. For example, if one’s Rabbi’s name is "Baruch," he may not refer to him in his presence as "Hacham Baruch." When one is not in his Rabbi’s presence, however, this is permissible. The Shach’s ruling would apply to a parent, as well. If one’s father’s name is Abraham, for example, it is forbidden to refer to him as "Father Abraham" in his presence, but this would be allowed when not in his presence.
Many other Halachic authorities, however, rule more leniently, and permit referring to one’s Rabbi or parent by his name when prefacing the name with a respectful title, even in the presence of the Rabbi or parent. The Kessef Mishneh (commentary to the Rambam’s Mishneh Torah by Rav Yosef Karo, author of the Shulhan Aruch) draws proof from the fact that Yehoshua, the disciple of Moshe Rabbenu, once addressed Moshe by calling to him, "Adoni Moshe" – "My master, Moshe" (Bamidbar 11:28). Apparently, it is permissible to address one’s Rabbi by his name – even in his presence – by prefacing the name with a respectful title, such as "Adoni." This is the ruling of the Peri Hadash (Rav Hizkiya Da Silva, 1659-1698), and this is the position accepted by Hacham Ovadia Yosef. Thus, it is permissible to address one’s Rabbi or one’s parent by his name even in his presence, as long as he uses a respectful title, such as "Rabbi," "Hacham," or "Father."
According to one view (cited by Pit’heh Teshuba, Yoreh De’a 240), if somebody is asked who his father is, he must add a title before mentioning his father’s name – such as "Father" or "Rabbi." However, Hacham Ovadia Yosef draws proof from many passages in the Midrashim that this is not necessary. For example, one passage tells of Moshe Rabbenu identifying himself as "the son of Amram," without saying "the son of my father, Amram." Likewise, Rabban Yohanan Ben Zakai identified himself as "the son of Zakai." Apparently, Hacham Ovadia explains, since one is identifying himself as the child, there is no need to add a respectful title, as it is clear that he intends no disrespect. This is, indeed, Hacham Ovadia’s conclusion, as cited in Yalkut Yosef (Kibbud Ab Va’em, p. 449; listen to audio recording for precise citation).
Summary: It is permissible to refer to one’s father or Rabbi by his name – even in his presence – as long as he adds a respectful title, such as "Rabbi Yosef," or "my father Yosef." If one is asked whose son he is, he may simply state his father’s name, and does not need to add a title.