Though it may sound surprising at first, a number of Halachic authorities addressed the question of whether a couple may get married if their fathers share the same name, or if their mothers share the same name. This question arises due to the Sava’a (Last Will and Testament) of Rabbenu Yehuda Ha’hasid (Germany, late 12th-early 13th century), which warns against entering a marriage if the mothers or fathers share the same name.
In truth, however, for Sepharadim there is no problem at all with such a marriage, as the Sepharadim never accepted the admonitions of Rabbenu Yehuda Ha’hasid’s Sava’a. And even among Ashkenazim, it is unclear whether Rabbenu Yehuda Ha’hasid wrote these instructions for all Ashkenazic Jewry, or only for the members of his family. Clearly, then, Sepharadim are not bound by this restriction at all. Furthermore, regarding such matters it is stated that "one who is not concerned, we are not concerned for him." Meaning, if a person does not feel that violating these warnings poses a risk, then the Rabbis do not instruct him to abide by them.
In fact, some draw proof to the permissibility of such a marriage from a story told in the Gemara (Berachot 42a) of Rabbi Yehuda who "made a wedding for his son in the home of Rav Yehuda Bar Hiya." It appears that Rabbi Yehuda’s son married the daughter of Rav Yehuda Bar Hiya, clearly indicating that a name shared by the two fathers (in this case, "Yehuda") does not disqualify the match. We should note, however, that Rabbi Haim Palachi (Turkey, 1788-1869) refuted this proof, noting that the Gemara perhaps meant that the wedding was held in Rav Yehuda Bar Hiya’s home, and not that Rav Yehuda Bar Hiya’s daughter was the bride.
In any event, as stated, Sepharadim are certainly not bound by this restriction.
This applies as well to another warning of Rabbenu Yehuda Ha’hasid, namely, that one should not marry somebody with the same name as his/her parent. Once again, an otherwise suitable match certainly should not be rejected due to such concerns.
In conclusion, it is worth noting the comments of the Noda Be’yehuda (Rabbi Yehezkel Landau of Prague, 1713-1793) regarding this topic (listen to audio recording for precise citation). The Noda Be’yehuda expresses his amazement over the fact that people do not hesitate to have their daughters marry ignorant, boorish men, without even thinking to consult a Rabbi, but become anxious when there is a potential issue concerning the name. The Talmud issues very stern warnings about allowing one’s daughter to marry an Am Ha’aretz (ignoramus), going so far as to compare it to placing one’s daughter in front of a lion. How ironic and baffling it is, the Noda Be’yehuda laments, that people pay more attention to a certain Rabbi’s will than to an explicit warning in the Talmud.
The Noda Be’yehuda thus urges one to maintain a proper perspective when marrying off a child, and to concern himself with the qualities and religious observance of the prospective match, rather than with hardly relevant issues such as the boy or girl’s name.
Summary: It is entirely permissible for a couple to marry if their fathers or mothers share the same name, or if the bride or groom has the same name as the other’s father or mother. In choosing a spouse for oneself or one’s children, attention should be paid to character and religious commitment, and not to names.