The Steamworks SDK has these functions in the IStreamFriends
// returns the local players name - guaranteed to not be NULL.
// this is the same name as on the users community profile page
// this is stored in UTF-8 format
// like all the other interface functions that return a char *, it's important that this pointer is not saved
// off; it will eventually be free'd or re-allocated
virtual const char *GetPersonaName() = 0;
// returns the current status of the specified user
// this will only be known by the local user if steamIDFriend is in their friends list; on the same game server; in a chat room or lobby; or in a small group with the local user
virtual EPersonaState GetFriendPersonaState( CSteamID steamIDFriend ) = 0;
// returns the name another user - guaranteed to not be NULL.
// same rules as GetFriendPersonaState() apply as to whether or not the user knowns the name of the other user
// note that on first joining a lobby, chat room or game server the local user will not known the name of the other users automatically; that information will arrive asyncronously
//
virtual const char *GetFriendPersonaName( CSteamID steamIDFriend ) = 0;
The Steam OnlineSubsystem uses GetFriendPersonaName only in the leaderboard and friends interfaces. So maybe you can get it through FOnlineUser::GetRealName()/GetDisplayName() instead (although this may only work for players on the friendlist).
If using the Advanced Sessions Plugin is an option, the Version Log states this