Name?

Pick your entity name and check that it's available. Before you decide on the name, check that the URL is available.

Name, Please?

1. Picking a Name. I agonize about naming things (or even people) every time I have to do it. In picking a name for a company, though, I've taken comfort in knowing that a name isn't necessarily forever: You can always rebrand with a DBA. With the potential impermanence as a security blanket, I try to think of a name that "makes sense" when you put a one-line description of what the company does after it, so that the reaction is "oh, I get it" when you add a tagline or explain the mission/product.
2. Check Domain Availability. You need email and probably a website, so once you have a potential name for your company, it makes sense to see if you can get a domain (xyz.com) that fits it. It seems like all one-word domains in English must already be registered by someone, so you may have to get creative. You can check whether a domain is available by searching on any domain registrar (e.g. Cloudflare or Google). IMHO, shorter is better. For example, if your company's named Exwhyzee Advisors LLC, and exwhyzee-advisors.com and exwhyzee-llc.com are both available, buy both, but use exwhyzee-llc.com (or even xyz-llc.com).
3. Check Entity Name Availability. You can't use a name that is already registered in your state or one that is registered nationally for a business that is similar to yours. Before you commit to buying the 5 related domains for your new company name, though, check that the name is available on your State's dept. of Corporations (New York or Delaware, for example). Also check the US Trademarks Office for any national registrations.