Rabbi Shemuel Pinhasi, in his work Haim Va’hesed (chapter 16), writes that after a person’s passing, Heaven forbid, the Maseva – the tombstone placed at the gravesite – should preferably be placed on the grave already on the seventh day after burial, and no later than the eighth day. According to the Zohar (vol. 1, p. 119), as Rav Pinhasi quotes, the Maseva should not be placed on the grave earlier than the seventh day, as this could be harmful. Therefore, the Maseva should be placed on the seventh day, after the mourners end the Shiba observance, when in any event it is customary to visit the gravesite. It should preferably be placed that day, and no later. This is the ruling of the Kuntras Ha’yehieli, and is the custom in Jerusalem. This is also the ruling of Hacham Ovadia Yosef (Yabia Omer, vol. 4) and of Rav Yitzhak Shehebar.

Rav Pinhasi notes the divergent customs of Ashkenazim and Sepharadim regarding the way the deceased’s name should appear on the Maseva. Sepharadim name the deceased and his or her mother, whereas some Ashkenazim mention the father. (Other Ashkenazim follow the Sephardic practice in this regard.) Thus, for example, Sepharadim would write on a tombstone "Yitzhak Ben Sara," whereas Ashkenazim would write, "Yitzhak Ben Abraham." The source of the Sephardic custom is the comment of Abayeh cited in the Gemara in Masechet Shabbat that whenever making reference to a person, one should mention the person’s mother. Rashi explains this to mean that the mother’s name should be mentioned whenever we pray for someone, and it is therefore customary, for example, to mention the mother’s name when reciting a "Misheberach" prayer for somebody. We apply this ruling as well to the Ashkaba prayer and the tombstone; in all these contexts, we mention the person and his or her mother. The reason, as explained by the Hochmat Shelomo commentary, is that the mother’s relationship to a person is definite beyond a doubt, while a father’s presumed relationship to his child cannot be conclusively verified. This is mentioned as well by the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909).

In any event, as mentioned, the accepted practice among Sepharadim is to mention the mother’s name in all contexts, including the inscription on a tombstone.

Summary: The tombstone should be placed on the grave on the seventh day, after the mourners finish the Shiba observance. It should not be placed before then, and this should not be delayed beyond the eighth day. Sephardic custom is to inscribe on the tombstone the deceased’s name and his mother’s name, such as "Yitzhak Ben Sara."