Q. Do you need to eulogize the departed one at the time of the unveiling of the matzeva? How about if the deceased did not like at all speeches and eulogies?
A. Recent Poskim do mention the tradition to say hespeidim and eulogies at the time of the dedication of the matzeiva, in honor of the departed and his family. (Menuchas Moshe 104, Levushei Mordechai 2: 140, Minchas Yitzchok 3: 51, Kol Bo and others).
Due to the tradition that hespedim are usually said, Poskim place restrictions as to when the hakomas hamatzeiva ceremony can be done, thus avoiding it in days when thachanun is not recited etc.
As far as the deceased disliking eulogies, likely it would follow the same rules as the hespedim said at the time of the levaya.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller and Horav Aharon Miller Shlit’a