1) The custom among Ashkenazim is not to name a child after a person who is still living,1 even if that person lives in another country.2 Some say that the objection is specifically to naming after one's father who is still living, but there is no objection to naming after other living relatives.3

2) The custom among Sephardim is not to be particular about this. On the contrary, they consider it to be a form of honoring one's father, and a protective charm for long life, if a grandchild is named after a living grandparent.4

3) Most authorities agree that one should not give his son the same name as his own.5 However, among the Yemenites, some do have the custom of giving children the same name as their own.6

4) If the child's maternal grandfather requests that his grandson be given his name while he is alive, there is no reason to forbid it.7

5) If one desires to name his son after his deceased father, but his stepfather — who has the same name — strongly objects, then he should not name the son after his father alone, but should add another name to it, and call the son by both names.8

6) If the child's paternal grandfather and his maternal grandfather have the same name,9 and one of them has died, and [the father] wishes to name the child after the deceased grandfather — if the surviving grandfather objects, then it is better to refrain from doing this, since most people would object to it. However, if the deceased grandfather had a nickname, the grandson should be called by this nickname. When the other grandfather passes away following a long life, they may then call the child by the original name also.10 Or else, they may change the grandson's name slightly,11 or give the grandson an additional name to be used together with the grandfather's name.12

7) A person who is in the process of dying (goses) is considered to be fully alive in this regard (even though most such people do die). A child should not be named after him until he has actually died.13