Two English names
In the United States the common name for the game with 2x12 pieces on the chequered 8x8 board is checkers, in the United Kingdom the common name is draughts. Both names are medieval. Checkers is a later form, the medieval form was at the checker.
The first reference of checkers dates from c. 1412:
(...) ydell dedys, that arn werkys of no profytz, as to pleyin at the tablys, at he chess & the chekyr, & at swyche vayn pleyis (...)
(Idle deeds that are works of no profit, like playing tables, chess and checkers and other vain games)
[Jacob's Well, c. 1412:105].
The first reference of draughts is from the first half of the 15th century too:
1620 Mony gaumes were begonnen the grete for to solas.
The chekker was choisly there chosen the first,
The draghtes, the dyse, and other dreg gaumes.
(Many board games were created for a greater enjoyment. First the chequered board was thought up, draughts, dice games and other games (with pieces?))
["The gest historiale of the destruction of Troy" c. 1440].
See for more information Stoep 2007:160-164.
We may suppose that the second name for the game was needed because of the introduction of a variety with the obligation to take under the penaly of the huff.