A PLAYER MISNAMES A DISCARD AND THE TILE IS IN THEIR HAND (Article 80) 

Commentary:  When a player misnames a discard and they have that tile in their hand, they do not need to switch the tiles. The player should name the discard correctly and the game should continue as normal.

Question from a player:  A player discards a tile but misnames it.  However, she has the correctly named tile in her hand.  Does she take the tile back and discard the named tile from her hand? 
 
Answer from the NMJL: Once a tile is fully named or touches the table the discarder cannot take it back. 

Source:  Mah Jongg Made Easy (2024 page 17, #4 in part); National Mah Jongg League Bulletin (2020)

Other answers from the NMJL: 

“You may not replace a misnamed tile with a tile from your hand. Once a tile has been discarded it must remain on the table as a discard but may be correctly renamed.” 

“You do not replace the tile with the named tile. misnamed tile is simply correctly named.” 
 
“A miscalled tile can only be called when correctly named. You do not take the tile back and you do not have to discard the named tile if you have it.” 
 
“A player may not take back a misnamed tile.  Down is down.  If the miscalled tile is called for mah jongg, the miscaller pays four times the value of the hand to the claimant.  Others do not pay.  The miscalled tile is called causing an invalid exposure, the calling player’s hand is now dead and there is no penalty to the discarder of the incorrectly named tile.”  
 
 Sources for other answers:  Mah Jongg Made Easy 2020 page 19 #7, National Mah Jongg League Bulletin Q&A (1998 page 5, 2004, 2005, 2012, 2014, 2015, 2018)