Baldur's Gate mints un-named trade bars, not coins
In current 5th edition canon, Baldur's Gate mints trade bars, and there aren't specific names.
Nothing I could find in Forgotten Realms lore suggests that Baldur's Gate minted coins in previous lore, although the FR lore base is so extensive, it is impossible to be sure.
A few third-party sources cite coin names for Baldur's Gate which cannot be traced to original sources, and appear to be non-canon, made up and perpetuated by fans.
Looking at 5e sources, the DMG, in Currency, mentions a number of places that mint their own currency, such as Sembia, Waterdeep, Silverymoon, and Cormyr, but does not mention Baldur's Gate.
However, it does say, under Trade Bars:
The city of Baldur’s Gate mints large numbers of silver trade bars and sets the standard for this form of currency.
Multiple 5e source books mention Baldur's Gate but do not reference coins minted there, including:
- Baldur's Gate: Descent into Avernus
- Candlekeep Mysteries
- Hoard of the Dragon Queen
- Sword Coast Adventurer's Guide
The Campaign Guide of the D&D Next playtest adventure Murder in Baldur's Gate mentions a professional guild, the "Financiers (bankers, moneychangers, and minters)", who, since they don't mint coins, must mint trade bars.
Additional Forgotten Realms lore
Looking a bit further afield, the Forgotten Realms wiki lists a number of places that mint coins, but again cites Baldur's Gate as minting trade bars. Citing the Forgotten Realms Campaign Setting 3rd edition as its source, it says:
For years, Baldur's Gate minted its own silver trade bars, the most common variety of which was a 1 lb (0.5 kg) bar worth 5 gp.
The wiki also says under Trade Bars:
Ranging in sizes from 1, 2, 5 and 10 lbs, trade bars were usually minted in silver, or more rarely, gold. Silver trade bars were worth 5 gp per lb, with the gold variety being worth 50 gp per lb.
Nothing is suggesting names for the trade bars.
Sources of unknown provenance
There are several documents available on the Internet that mention coins used in Baldur's Gate, known as the head, the sword, and the double-eagle.
"Currencies of the Forgotten Realms", on naturalcrit.com
This document, Currencies of the Forgotten Realms says Baldur's Gate uses coins named head, sword, and double-eagle, although it cites no sources, and is posted on naturalcrit.com, using The Homebrewery, which "makes the creation and sharing of authentic looking Fifth-Edition homebrews easy".
Lacking references, it seems unofficial.
"Coins of the Forgotten Realms", on angelfire.com
And Coins of the Forgotten Realms also says Baldur's Gate uses coins known as head, sword, and double-eagle.
The document says:
This information originally appeared in the FORGOTTEN REALMS Adventures hardbound book
and says it was downloaded from TSR and cites copyright TSR 1990 and 1996.
It also says that the material is:
a mixture of material published by TSR and my own creation
A perusal of the Forgotten Realms Adventures book in PDF form (copyright 1990) supports that Baldur's Gate mints trade bars but does not support that it mints coins.
I mention these documents for completeness, but I am unable to confirm the coins named with official sources, so I have to conclude that these coin names seem unofficial.
(Thanks to Groody the Hobgoblin and Exempt-Medic for their research.)