For many years, members of the genus Agaricus were given the generic name Psalliota, and this can still be seen in older books on mushrooms. All proposals to conserve Agaricus against Psalliota or vice versa have so far been considered superfluous.
Several origins of Agaricus have been proposed. It possibly originates from ancient Sarmatia Europaea, where people Agari, promontory Agarum and a river Agarus were known (all located on the northern shore of Sea of Azov, probably, near modern Berdiansk in Ukraine). Note also Greek ἀγαρικ όν, "a sort of tree fungus" (There has been an Agaricon Adans. genus, treated by Donk in Persoonia 1:180.)
Dok reports Linnaeus' name is devalidated (so the proper author citation apparently is "L. per Fr., 1821") because Agaricus was not linked to Tournefort's name. Linnaeus places both Agaricus Dill. and Amanita Dill. in synonymy, but truly a replacement for Amanita Dill., which would require A. quercinus, not A. campestris be the type. This question is compounded because Fries himself used Agaricus roughly in Linnaeus' sense (which leads to issues with Amanita), and A. campestris was eventually excluded from Agaricus by Karsten and was apparently in Lepiota at the time Donk wrote this, commenting that a type conservation might become necessary.
The alternate name for the genus, Psalliota, derived from the Greek psalion/ψάλιον, "ring", was first published by Fries (1821) as trib. Psalliota. The type is Agaricus campestris (widely accepted, except by Earle, who proposed A. cretaceus). Paul Kummer (not Quélet, who merely excluded Stropharia) was the first to elevate the tribe to a genus. Psalliota was the tribe containing the type of Agaricus, so when separated, it should have caused the rest of the genus to be renamed, but this is not what happened.