Is there is a name for class of businesses which make custom clothes?

Hi! You might say “clothier” or “custom clothier.” Also, depending on what types of clothing the business makes, you could say “custom dressmaker,” “suitmaker,” etc.

Amy

I think you could say “tailor,” but as you point out, this might refer to someone who just alters or repairs clothes, rather than someone who actually makes custom clothing.

Also, you needn’t say “tailor shop.” We can just say “the tailor” or “a tailor” (if not refering to a specific tailor’s shop), as in, “I need to take this dress to the tailor to be hemmed.”

Amy