It is customary among Sepharadim to name a child after a grandparent even during the grandparent’s 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 – the father’s father – who has the same name. The Shulhan Aruch rules that the obligation of "Mora Ab" – to have reverence for one’s father – forbids calling one’s father by his name, or even calling out to somebody else by the same name in his father’s presence. How, then, can a father call to his son in the grandfather’s presence, if the grandfather has the same name?
One solution that has been proposed is for the grandfather to express his Mehila – meaning, to declare that he waives the son’s 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 one’s 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 son’s 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 boy’s name in the grandfather’s presence. For example, if the son’s name is Abraham, he can call him "Avi," or, if it’s Yosef, he can call him "Yoss." The advantage of this method is that one not only avoids the prohibition of using his father’s 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 father’s Mehila, and to instead make some change in his son’s name.
When a father names his child after his father, he ends up mentioning his father’s name at the Berit, when announcing his child’s name. And if the baby’s father himself is named after his father’s father, then his child’s name will be precisely the same as his father’s 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 – other than the infant’s father – should announce the name, as the father should not mention his father’s name in his presence.
However, Hacham Yishak writes that this ruling is "a Peleh" ("baffling"). If a father is giving his child his father’s 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 one’s father’s name, which is entirely permissible in one’s father’s 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 child’s name at the Berit, even if the name is precisely the same as his father’s and his father is present.
It should be noted that if one signs a Ketuba – when it is customary to identify oneself by his name and his father’s name (e.g. "Eliyahu Ben Yosef") – it is entirely permissible to write out his name and his father’s name. As the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) writes (Parashat Shofetim), writing one’s father’s name does not violate the prohibition of calling one’s father by his name.
Summary: It is forbidden to mention one’s father’s name in his presence, even if he is calling somebody else. If one’s son has the same name as his father, it is proper to use a slightly different name when calling his son in his father’s 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 father’s name.
