There are numerous domain name registrars. Listed below are just a few, along with my comments, if I know anything about them. Note that the domain name industry is highly competitive, with prices wildly fluctuating throughout the year, every year, so it's impossible to really mention accurate prices below unless I spend all my time updating this page. Please check their sites for the latest rates. All prices below are in US dollars.
Sedo is where I bought my domain - over Escrow - and is a global marketplace to buy, sell, and park domain names. They've over 18 million domain names for sale, but the big part is that they're a huge, well-respected company. This may not be important if you're spending $150 on a domain, but in a $15,000+ purchase - which happens in many cases - you will be potentially buying from a foreign entity, that you don't know, and many of them will suggest an escrow payment. This means you put the money in an account owned by a third party that will hold it and only pass it on once the domain has been transferred over into their name (which in this case is what Sedo does). This can be quite disconcerting - but Sedo is well-known and has done many, many deals - and the process is about as full of hand-holding as handing tens or hundreds of thousands of dollars for a domain name can be.
Just days after Verisign launched the Site Finder Service, ICANN wrote a strongly worded letter ordering them to disable it. Verisign complied, but not without writing a strongly worded letter of their own, in the form of a lawsuit. Verisign argued that ICANN overstepped their bounds in trying to control their activities, and ICANN argued… that Verisign overstepped their bounds in performing those activities.
Absolutely. Owning 'yourname.com' (as well as related domains such as yourname.tech or yourname.me) is a great way to brand yourself and retain control over your name's online presence. With a personal domain name, you can set up a portfolio, blog, or hobby site that’s associated with your own personal life. You can also set up a custom email address like firstname.lastname@example.org allowing your visitors an easy and memorable way to reach you. So even if you have no immediate use for yourname.com, it's wise to register a personal domain to ensure that you (and not some stranger) control your name online.