As the title says, would there have been brands of carriages as there are now with cars? When and where?
Absolutely. Brewster & Company was the finest maker of carriages in NYC during the carriage era and very well known. Each major city certainly had its famous carriage building firms. Studebaker was one of the United States largest producers before the car era took over. Many of the body makers for the early cars were formerly large carriage manufacturers (Hooper, Million-Guiet, Holland & Holland). There were many, many styles of carriage in near infinite variety of appointments and accessories from thousands of companies large and small. Fine carriages were very richly appointed and custom painted in the owner's colors.