During the League One match between the two teams at Kingsmeadow on September 22, the hosts' Twitter account referred to the visitors as "Milton Keynes" throughout.
Furthermore, Wimbledon's matchday programme made no reference to their opponents.
The rivalry between the two teams stems from the original Wimbledon club, who won the FA Cup in 1988, relocating to Milton Keynes in 2003 and assuming a new name.
An EFL statement read: "The EFL has been in communication with both clubs and, as a result of the positive dialogue, a decision has been taken to drop the charges against AFC Wimbledon on the proviso that all parties will now enter into discussions using their best endeavours to seek to reach an agreed position between the parties for the future.
"Those discussions will be in the form of mediation which will be facilitated by the EFL."
AFC Wimbledon, who lost the game 2-0, were warned over a similar offence in the 2016-17 season.