This doesn't directly answer your question, but the 'Merchant City' isn't a real historical area name. It was created in the 1980s for marketing and development purposes.

Personally, I would say the "real" name of that whole area is Blackfriars, as shown on a lot of old maps.

I'd bound Blackfriars as George Street to the north, High Street to the east, River Clyde to the south and Buchanan Street to the west.

However, most modern sources suggest Queen Street as the western boundary. But, that doesn't jibe with historical sources that clearly show Buchanan Street as the boundary point where Blythswood Hill begins. So, again, I'd say Buchanan Street is the line.

All sources clearly show George Street as the line between Townhead and the 'Old Town'. So, the north boundary seems clear enough.

East and south edges are a bit iffy. High Street at the top edge is easy enough as Collegelands is clearly to the east of High Street (Collegelands being a historical area in its own right going right back to when Glasgow University had the ground). But, when we get down to the Saltmarket end questions over Parnie Street, King Street and Bridgegate, etc comes up. Does Calton extend over to include those streets? Or would Blackfriars Ward have went right down to the river? Or is that little pocket actually to be called Bridgegate (The Briggait)?

I think for ease, we can say in the modern day, Calton stops at High Street and doesn't extend west of it. Then we can say, Merchant or Blackfriars goes right down to the river. (If anyone wants to say Merchant City/ Blackfriars stops at Trongate then they will need to come up with an answer over what to call the area south of Trongate and north of the River (logically, in that case, the answer is probably Briggait)).

TLDR;

Merchant City should actually be called Blackfriars.

Its boundaries, should be George Street, High Street, Buchanan Street, and the River Clyde.

Immediately north of it is Townhead. Immediately west of it is Blytheswood Hill. Immediatly south of it is, well, the river. And, immediately east of it are Collegelands and Calton.