It's an everburning question - for some of the gamers including me. I asked, too, but "currency" seems not to be on the bill board list top 100.
At the start of the Council of Thieves campaign, I posted a poll to my players, giving them a chance to "win some extra money to equip the PCs" providing me with the best suggestions for the currency of Cheliax (and some other realms/nations).
The names below attracted my interest and won the poll (the prize was one coin of the same name for every winning entry):
Default: Platinum, Gold, Silver, Copper
Andoran: Eagle, Falcon, Hawk, Sparrow
Cheliax: Pact, Debt, Deal, Favor
Isger: Devil, Hellhound, Imp, Tiefling
Korvosa: Crown, Sail, Shield, Pinch [some of that is official, see Guide to Korvosa]
Molthune: Soldier, Citizen, Laborer, Farmer
Nidal: Master, Shadow, Serf, Skeleton
Rahadoum: Keeper, Lawyer, Council, Elder
Taldor: Star, Crown, Moon, Honor
Besides, the module Tower of the Last Baron provides you with the denomination of Andoran silver, named Silver Crown.
Yeah would be nice if the companion books had, had a little blurb about coin names. I think it adds a little something if each country uses different names for coins.