Your business name is your brand, so take your time to pick the right name that you feel good about.
Most designers want to use their own name as a brand name, which is great but there is one caveat.
If you decide to sell your company down the road, the buyer will own your brand name i.e. your name. And you would not be able to use your name again for other fashion line or other business, depending on how it is set up.
So, be careful when picking a brand name and if you do want to use your own name as consult with a lawyer about ins/outs of it.
Start with checking if the name is available:
1, Check Trademark availability
Go to https://www.uspto.gov/trademark and check if the trademark is available for your brand.
2, Domain name availability
• Go to hostgator & click on Domains section to check if the domain is available, OR
• Go to Godaddy to check domain availability and purchase your domain.
• Check for .com, .co etc. names in case you want to purchase those to make sure no one else uses your brand.
3, Social accounts availability
• Also, go thru all the social accounts that you want to create and see if the names and URLs are available. This will help you maintain brand identity thru all the platforms. such as Facebook, Pinterest, Linkedin, Instagram, etc.