If your concerned people may try to delete a name that is logged within gaming sessions, then just either state a warning when someone wants to delete one or prohibit deletions if name has 1 or more games played. If zero plays then should be allowed to delete the entry.
We will definitely add features for deleting gaming groups, games, and players. We just added the ability to delete a Player if it doesn't have any games but we'll keep adding more powerful/permanent delete options in the coming months as there is a high demand for this.