1&1 Internet — This is primarily a large web host that is also a domain name registrar. Like all registrars, there are different charges for different domain suffixes. For example, at the time I last checked, you pay $0.99 for a ".com" on your first year, then $14.99 per year thereafter. The fee includes private domain registration, which means that your particulars are hidden from public view (done by registering the domain in the name of a proxy company). You also get a free email account and unlimited email forwarding, DNS management, a free SSL certificate for your domain, etc. Both credit card and PayPal payments are accepted by this registrar.
Keep in mind, however, that free domain names are usually free only for one or two years, after which the registrar will bill you for the annual or biennial fee. In other words, the provider of the free domain name pays only for the first billing from the registrar. Also take note of whether or not the provider charges a fee for setting up a domain name. Most services offer to transfer an existing domain name to their servers at no cost, but sometimes you'll find a setup fee over and above the registrar's fee.
Critics often claim abuse of administrative power over domain names. Particularly noteworthy was the VeriSign Site Finder system which redirected all unregistered .com and .net domains to a VeriSign webpage. For example, at a public meeting with VeriSign to air technical concerns about SiteFinder, numerous people, active in the IETF and other technical bodies, explained how they were surprised by VeriSign's changing the fundamental behavior of a major component of Internet infrastructure, not having obtained the customary consensus. SiteFinder, at first, assumed every Internet query was for a website, and it monetized queries for incorrect domain names, taking the user to VeriSign's search site. Unfortunately, other applications, such as many implementations of email, treat a lack of response to a domain name query as an indication that the domain does not exist, and that the message can be treated as undeliverable. The original VeriSign implementation broke this assumption for mail, because it would always resolve an erroneous domain name to that of SiteFinder. While VeriSign later changed SiteFinder's behaviour with regard to email, there was still widespread protest about VeriSign's action being more in its financial interest than in the interest of the Internet infrastructure component for which VeriSign was the steward.
If you already have a web host, obtain from them the names of their primary and secondary nameservers. Don't worry if you don't understand what these things mean. Just save the information somewhere. The information can usually be obtained from their FAQs or other documentation on their site, usually under a category like "domain name" or "DNS" or "domain name transfer" and the like. If you can't find it, email them. You'll need the information to point your domain name to your website after you buy your domain. Having said that, if you don't have a web host yet, don't worry. Just read on.
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 email@example.com 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.