CEO of Zapaty, Creator of the Idea Machine, Author of "The Doer of the Most Important Stuff" (available on Amazon), and Lover of Banana Pancakes.
If you consider yourself one of the best (which I assume you do, given that you're looking for high-paying clients), you should look into TopTal https://www.toptal.com/talent/apply
TopTal is a freelance site similar to UpWork, Freelancer, Odesk, etc...the difference is, TopTal ONLY hires the top 3% (so bring your A++ Game) and they only allow the top companies to hire their freelancers, so you don't have to worry about competing lowball bids to get work. Supply is low, demand is high, and you could literally pick up full time work immediately after being approved. The application process is pretty intense but if you get through it it's worth it. They are rabidly looking for UI & UX designers.
If you're not already using Upwork, I would get on there too. Some of the companies on there are looking for quality over price and willing to pay more for good work, but the demand is much lower.
Choosing a business name is a real hang up for some people. I've met would-be entrepreneurs that get so hung up on the perfect name that they never start! That being said a great name is very important. Gone are the days when a name has to have any industry specific meaning (look at Google, Twitter, Apple, etc). In my opinion Logixess and Logixeed are a little hard to pronounce and do not roll off the tongue. Below is a link to a great tool for choosing a name, which also gives you available domains. I created the name for my company "Zapaty" with this tool. Best of luck! Here is the link. http://www.bustaname.com/word_maker
If you have any more questions, feel free to reach out.