Ask HN: Business name availability?

I found a name for my company that I want to make. I recently found that the name is trademarked in two different places:

Fixed price graphic artistic design services for small task design projects.

Clothing, namely, t-shirts, shirts, tank tops, sweatshirts, sweaters, jerseys, jumpers, pants, sweatpants, shorts, skirts, dresses, jackets, coats, vests, underwear, socks, warm-up suits, bodysuits, leotards, tights, leggings, leg warmers; headwear, namely, hats, caps, toques, visors, headbands, bandanas; clothing accessories, namely, belts, scarves, shawls, shoulder wraps, arm warmers, mittens, gloves; sandals

------------------------------------------------------------

No company has the name that I want, these are both products of companies. I want to name it Example, LLC.

My company is about making apps for iOS. Will I be able to get it without being sued?