A shop name on Etsy does two jobs at once. It identifies your store, which is a retail service, and it usually ends up on your products and packaging, which makes it a product brand too. Trademark law treats those as two different things, and rights owners complain about both.
The two classes that matter
Retail services sit in class 35. A registered mark in class 35 for online retail can be used against a shop name even if you sell completely different goods from the owner.
Your products sit in their own class: 25 for clothing, 14 for jewellery, 21 for mugs, 16 for prints and paper goods, 20 for home décor. A mark in your goods class can be used against your shop name the moment it appears on a product or a label.
So the check is two checks. The name against class 35, and the name against the class of what you sell.
Run it before launch, not after
Type the shop name into the checker above with Etsy selected; the goods classes are preset to the categories Etsy sellers use most. Add class 35 in the advanced options. Set the territories to where you ship, which for most Etsy sellers means the United States, the United Kingdom and the European Union at least.
What you want to see is nothing close in your classes, or only dead marks and unrelated goods. What you do not want is a live mark that sounds like your name in class 25 or 35 owned by a company that sells online. Those owners search Etsy.
What happens if you skip it
The usual path is a complaint against one listing, then a second, then Etsy asks you to rename the shop or suspends it. By then the name is on your labels, your Instagram, your domain and your thank-you cards. Renaming a launched shop costs a week of work and some of your search ranking. Checking a name costs a minute.
Naming that survives the check
Coined words survive better than dictionary words. Two-word names where neither word is a known brand survive better than one distinctive word. Your own surname survives well in most countries, as long as it is not already a brand in your goods. And anything that references a franchise, a team or a celebrity does not survive at all.