Title says it all, the profession shown in a villager's name is incorrect.
I run the MCA 1.12.2-6.1.0 version of the mod, the following fix from the 1.12.2-6.0.1 version is not present-

"Career names and IDs were not matching in the Trade GUI."
-They are not matching in the Trade GUI for 6.1.0

This issue is with every profession that has career variations-

Leatherworkers have the inventory of Butchers
Butchers have the inventory of Leatherworkers

Fishermen have the inventory of Farmers
Farmers have the inventory of Fletchers
Fletchers have the inventory of Shepherds
Sheperds have the Fisherman's inventory

Cartographers have the Librarian's inventory
Librarians have the Cartographer's inventory

Armorers have Toolsmith inventories
Weaponsmiths have Armorer inventories
Toolsmiths have Weaponsmith inventories

-this issue can be replicated easily and also effects villagers from other mods, ONLY if they are one profession with
careers, for example-

Villagers from immersive engineering will be effected when MCA is installed, engineer is a profession with 4 or so careers,
Necromancers from Villager Trade Tables will end up with Cleric inventories, and Clerics with Necromancer inventories,
as Necromancer is a career variation to Cleric when that mod is installed.

-this is not an error or bug due to other mods installed, this issue is within MCA itself, and how it handles career names/career inventories. The issue is not present when a profession only has one career. If I knew what to fix/edit within MCA itself I would do this myself, but I have no idea of what file I'd need to work with to correct the villager's profession names to match their inventories.

(Pictured below is an "Armorer" but with the inventory of a Toolsmith)
(An actual Armorer ingame would have an iron helmet as their 2nd trade option,
however, only "Weaponsmiths" have Armorer inventories)

Me too, which makes me very distressed. What they can trade doesn't match their profession

To further add, I can replicate this issue, any time I create a custom villager that becomes a "variation" of a career. For example let's say I make a villager profession called "Necromancer" and I make it become a variation of the Priest career, all actual "priests" will end up as "necromancers". The issue is within MCA itself and how it handles professions and careers.

(Me making custom villagers does not involve editing MCA, as the only thing I know to do in edits is to add in skins and what villager careers will use them, along with giving villagers from other mods an assignable skin, me making custom villagers is another mod.)

Edit: To further add, the only current version of MCA that even gets their professions right is MCA-1.12.2-6.0.0-beta, but this version is even WORSE. It removes female bodies for starters, the villager editor loses the feature to assign skins manually, and this version is not an option for my 2 yr old server that runs MCA-1.12.2-6.1.0, as attempting to use 6.0.0-beta causes villagers' professions to become their names.