My spouse has a living relative with the same name as my deceased relative. My spouse has a living relative with the same name as my deceased relative.
Ashkenazic custom discourages naming a baby after a living relative.
This is a based on a folk-myth that this might confuse the Angel of Death, who might then accidentally take the baby instead of the older relative. Sefardic custom has no such tradition, and thus encourages parents to name their children after living relatives. Generally, Ashkenazi Jews should follow the traditional Ashkenazi custom, and Sefardic Jews should follow the Sefardic custom, but the end decision is left to the parents. For the most part, most people would not use the same name. However, as with anything, there are solutions.