When in Charm Parties, players will see the names of the players who have gifted Charms with the option to thank them.
However, players do not see this option next to their own gifted Charms. It will just appear like a normal Charm.
The reason a player's own Charms appear like this is because a player doesn't have the option to thank themselves for gifting Charms. However, other players will still see that option normally as well as who is gifting the Charms.