Final answer:
The term that best describes the recognition of a designer's merchandise being featured in a store catalog along with a substantial payment is 'royalties'. Royalties are continuous payments received based on the sales or usage of the designer's work.
Step-by-step explanation:
When a designer's merchandise is featured in a store catalog and they are paid a substantial amount for this recognition, the term that best describes this recognition is royalties. Royalties are payments made to a creator of a product, like a designer, for every piece of their work that is sold or used.
It's a continual source of income that correlates with sales or usage. Stipend, patronage, and grant don't fit as well into this context as they have different financial implications. A stipend is typically a fixed sum of money paid at regular intervals, patronage involves financial support without direct compensation for individual sales, and a grant is a sum of money given for a specific purpose that does not need to be paid back and is not typically related to sales.