Merch by Amazon reviews the brand field on every design submission, and it is the field sellers think about least. They spend hours on the artwork and type the brand name in ten seconds.
What the review checks
The brand name is compared against trademark registers, mostly the USPTO for the .com marketplace and EUIPO plus national registers for the European ones. A match with a live mark in class 25 (clothing) or the related classes for the product type you chose gets the design rejected at review. A near match, one that looks or sounds like a known brand, gets flagged too, especially where the brand is well known.
It also checks for brand names that reference other brands: anything with a franchise name, a team, a celebrity, or a phrase like "Nike lovers".
What passes
Coined words with no meaning. Two-word combinations where neither word is a brand. Descriptive names that do not claim a brand, such as "Funny Cat Tees", as long as the words are not themselves registered. Your own name, if it is not already a brand in class 25.
What passes today can still be complained about tomorrow. Review is a filter, not a clearance.
Check before you submit
Type the brand name into the checker above with Merch selected. It sets the classes to 25, 24, 18 and 21 and the territory to the United States, which you can extend to the EU and the UK if you publish there. Look for live marks with a high score. If one exists, choose another name. It takes less time than a rejection and resubmission cycle, and it does not count against your slots.
Then run the design text through the same checker. Brand and design are reviewed separately, and a clean brand name does not save a design that quotes a registered phrase.
One brand or many
A single brand across all your designs builds recognition and is easier to register later. Many brands spread risk: one complaint takes down one line, not the whole account. Whichever you choose, check each name once, and keep the checker report. If Merch asks why you believe you can use the name, a dated report showing no live conflicts in class 25 is the answer they are looking for.