Sefardim engrave on the Matzeiva, the name of
the Niftar and the Niftar’s mother's name.
Ashkenazim engrave the name of
the Niftar and the Niftar’s father's name.
Recently Ashkenazim have a Minhag to add another
line at the bottom, and write Sheim Imoi/Imoh -----
The vast majority of the old Kevorim in Eretz Yisroel
had no engraving at all.
Rabbi Yechiel Michel Tukachinsky zt"l, writes*, in the year 1928,
the Jerusalem Museum exihibited old coffins and bones
which were found on Har Hatzofim. He went with Rav A.Y.
Kook zt”l and managed to convince the Museum to
return the bones for reburial.
(interesting- quiet Shtadlonus without public protests & riots,
can sometimes be effective as well)
The Museum insisted to keep the coffins. R.Y.M.T. noted
there were 23 coffins, from two families. 10 came from
one family and 13 from the other family.
4 of the 10 had engraved only the name. (Yehuda, Chana,
Miriam, Yehuda) The other 6 had no engraving at all.
The other family had all 13 coffins engraved. Two had
names without the father. Three had the name followed by
the word” Ben” (son) fathers name was illegible. Two women
both were called Shalom. One was Eishes Yehudah, the other was
Eishes Elozor. One was Shimon Avi (father of) Yosef. The other
five had their names the sons of their fathers.
These coffins were from Zman Bayis Sheini and followed
the Ashkenazi Minhag of naming the father, not the
Gesher Hachayim 2 p205