Conventions in the naming of children differ greatly between Sephardim and Ashkenazim and these have significance to the genealogist. The first that comes to mind is that Sephardim name children after persons who may be living or dead whereas Ashkenazim name their children after relatives that have died. Among Sephardim, the convention is to name the eldest son after the paternal grandfather and the eldest daughter frequently after the paternal grandmother.
Therefore, whereas in Ashkenazi research the date of birth of a child can sometimes be used to guess at the approximate year of death of the namesake, in Sephardic genealogy the name of the eldest son gives clues to the name of the paternal grandfather. This fact can sometimes be of great help in differentiating family trees.
Common Sephardic naming conventions (also see [http://www.sephardicgen.com/yohasin.htm Jewish Names]):
Firstborn son named after the paternal grandfather,
second male child after the maternal grandfather,
first daughter named after the paternal grandmother,
second female child after the maternal grandmother,
next child after the paternal uncle or aunt,
next after maternal uncle/aunt,
If a grandparent (paternal or maternal) or sibling was deceased, his/her name would often take precedence over the living relative. Some Spanish exiles named children after their own parents*.
* I suspect this was the case in our family.
We have also our own tradition of naming the first-born Elias (Elia, Elie, Eli) or any variation as, for women, Elisa, Elisabeth, Eliane, Liana, etc. The first name Elias would be always compose with a second name, after the father or grandfather... Which one, this is something we have to analyse to be sure.