The letters at the end of a domain, like the .com in Bitly.com, are called the Top-Level Domain (TLD). There are over 1,500 TLDs (though not all are available for use).
Most that you use will either be country specific (all two-letter TLDs are reserved for countries) or newer, topic-focused TLDs (.xyz, .plumbing, .store, etc).
Each TLD is operated by a different entity and may have its own rules for who can buy or use domains under their TLD. Some are very permissive and you just need to pay (.com, .io, .ly), while others are more restrictive and may be hard to obtain. For example, Ireland (.ie) strictly requires that the content on .ie sites be relevant for people in Ireland.
Keep these things in mind as you choose and set up a custom domain:
- The domain for your short links must be different than your website domain.
- It can't be more than 32 characters long, including the dot.
- If you don't have one yet, Bitly offers a complimentary domain on some paid plans.