This was the theme of the first week in February - with the prompt being "Do you share your name with an ancestor? What about a name that keeps repeating itself in your family tree? Do you have an instance of ancestors naming two children the same? (It happened more often than you might expect!)"
I can say that at least with Ashkenazi Jews you don't name after living relatives, however certain naming conventions have definitely helped in my research. Which I may go into later.
While deep diving my German Jewish ancestors I found a number of instances of duplicate children from the same parents with the same name.
Two specific examples of this that come to mind are with my 3rd great grandparents Moses Levy and Regina Mendel and Regina's parents Andreas Mendel and Amalie Benedict. Before FamilySearch changed their film lending policy I was able to acquire scans of of various BMD records.
While researching Moses and Regina (along with the other Jews in Duisburg, but that's a different story) I discovered that they had 2 children that did not live to adulthood - named August/Gustav, obviously similar if not the same. August happened the to be the name of Regina's uncle though he had died a few years after Regina's children were born and died so it's a little weird considering the Jewish custom of not naming after living relatives. Perhaps there is another August or Gustav (or similar name) that I have not found yet, which makes sense as to them having cousins named August or Gustav born before the Regina's uncle died. The only exception to this that I have seen is in the Netherlands.
The other instance in my German research I have seen is with Andreas and Amalie's children, of which there were 16. Their first and ninth children were named Salomon. Probably for Amalie's father Salomon, who died in 1812 before they were married.
And while writing this a third, and the most curious, instance of this came to mind.
While researching the the family of one my sets of 6th great grandparents in Amsterdam a previous researcher found that there were two living brothers named Salomon which even in the Netherlands is inexplicable. If there wasn't such as big age difference I would have assumed they were the same person. Maybe one of these days, now that Amsterdam BMD records are more easily accessible via the internet, I will dig deeper.