This is a fairly straight forward question. I am under the impression that this is bad. This is why you don't see many Moishe Abromowitz, III.
Why is this bad, and why isn't that practice carried thru out of Judaism?
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Naming children after the living is only discouraged among Ashkenazi Jews; among Sefardim it's not uncommon.
Sephardi Jews also name children after relatives who are still alive. This source is from the Talmud, which records a child named after Rabbi Natan while he was still alive (Shabbat 134a)
The reasons why Ashkenazim don't are: (From Chabad.org)
- Since it is a widespread custom to name children after deceased parents, grandparents and great-grandparents, naming after a living one could appear as though you're waiting for that person to die, G-d forbid.
- Out of respect for our parents, we don't refer to them by their proper names. Some say that when in the presence of a parent, you shouldn't use that parent's name even to refer to somebody else. For example, if your mother is named Sarah, you shouldn't refer to your friend who is also named Sarah by name in front of your mother. If we would name our children after our living parents—well, you can imagine the conundrum, and inevitable trip-ups.
Sources are brought at the bottom of that page.
For more information, check out those two links.
Among Ashkenazim it is generally regarded as an 'Ayin Hara' (Evil Eye). Among Sephardim it is the opposite - it is regarded as a way to confuse the angel of death, because he cannot take the wrong person.
(Source: several Sephardim I've spoken to about the subject)