It is customary among Sepharadim to name a child after a grandparent even during the grandparentís lifetime, and so it is quite common for children to have the same name as their grandparents. This gives rise to an interesting Halachic question as to whether the father in such a case is permitted to call his son by his name in the presence of the grandfather Ė the fatherís father Ė who has the same name. The Shulhan Aruch rules that the obligation of "Mora Ab" Ė to have reverence for oneís father Ė forbids calling oneís father by his name, or even calling out to somebody else by the same name in his fatherís presence. How, then, can a father call to his son in the grandfatherís presence, if the grandfather has the same name?
One solution that has been proposed is for the grandfather to express his Mehila Ė meaning, to declare that he waives the sonís obligation not to mention his name in his presence. However, this solution hinges on a debate among the Halachic authorities as to whether Mehila is effective even for the obligations of "Mora Ab," or only for those obligations that fall under the category of "Kibbud Ab" (showing respect for oneís parent). According to the view that Mehila does not absolve a son of his "Mora" obligations, it would not help for the grandfather to waive the sonís requirement to avoid using his name in his presence.
A second option that the Poskim suggest is for the father to make some kind of change in the boyís name in the grandfatherís presence. For example, if the sonís name is Abraham, he can call him "Avi," or, if itís Yosef, he can call him "Yoss." The advantage of this method is that one not only avoids the prohibition of using his fatherís name in his presence, but also fulfills a Misva by specifically using a variation of the name out of respect for his father. Accordingly, Hacham Yishak Yosef writes (listen to audio recording for precise citation) that it is commendable for the father not to rely on his fatherís Mehila, and to instead make some change in his sonís name.
When a father names his child after his father, he ends up mentioning his fatherís name at the Berit, when announcing his childís name. And if the babyís father himself is named after his fatherís father, then his childís name will be precisely the same as his fatherís name. Accordingly, Hacham Bension Abba Shaul (Israel, 1924-1998) ruled that if the grandfather is present at the Berit in such a case, somebody else Ė other than the infantís father Ė should announce the name, as the father should not mention his fatherís name in his presence.
However, Hacham Yishak writes that this ruling is "a Peleh" ("baffling"). If a father is giving his child his fatherís name, this is clearly done as an expression of respect for his father, and thus announcing the name cannot possibly be interpreted by anybody as a lack of reverence for his father. This is no different than reciting text from the Tanach or a prayer that contains oneís fatherís name, which is entirely permissible in oneís fatherís presence, as it is obvious that there is no lack of reverence intended. Therefore, Hacham Yishak rules (listen to audio recording for precise citation) that a father may announce his childís name at the Berit, even if the name is precisely the same as his fatherís and his father is present.
It should be noted that if one signs a Ketuba Ė when it is customary to identify oneself by his name and his fatherís name (e.g. "Eliyahu Ben Yosef") Ė it is entirely permissible to write out his name and his fatherís name. As the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) writes (Parashat Shofetim), writing oneís fatherís name does not violate the prohibition of calling oneís father by his name.
Summary: It is forbidden to mention oneís fatherís name in his presence, even if he is calling somebody else. If oneís son has the same name as his father, it is proper to use a slightly different name when calling his son in his fatherís presence. For example, he can use "Avi" instead of "Abraham." If a father is naming his son at the Berit after his father, he may make the announcement, even though he is mentioning his fatherís name.