Lotsa good advice, but in case you meant exactly what you wrote
such as a table containing only mentee name and start/end dates
then no. You would use the menteeID from that parent table, not duplicate the name in both tables. Same goes for other similar situations. Reason being is that you otherwise have to be concerned with updating ALL instances of a value when the value is changed in the parent source. Suppose Mary Brown gets married and takes the spousal last name (Smith). While you can address the issue via cascading updates in your relationships, it would mean these have to be a) established and b) all encompassing (better not miss any). Some developers don't bother with relationships, and don't have to be concerned with cascading since they'd use the ID in all "child" records.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.