Historically, hereditary land tenure has been referred to as a domain. These could include both land and buildings, whole cities and fortresses. Today we understand only one thing by this word - the name of the site.
So, each site has a domain and this is its unique name. By domain, each site is identified in the entire mass of sites that are on the Internet.
What domains can there be? Top-level domains (for example.ru,.com,.gov, and so on) can be national (ru, rf) or general use (com, net, org). A national domain can indicate belonging to a particular country, but also to a region. Within these domain zones, individuals and organizations register their domains of lower levels.
Most reputable site owners try to register names for their sites in the domain zone that will indicate either the country in which the target audience of the site is located, or in the one that will indicate the profile of its activities in some way. Another option for choosing a site name is to create a funny or beautiful "phrase". A typical example is zajcev.net. Thus, it is already clear that you can compose a name for the site yourself, but we must not forget that if such a name already exists, then you cannot choose it.
What else do you need to remember before registering a domain? The domain can be both foreign language and Cyrillic. It is better to come up with a name for the site as short and capacious as possible, so that it is well remembered and easy to type. You can check if the site name you have invented is already taken from a Russian domain name registrar, for example (https://www.nic.ru/dns/).
By the way, the memorable and original name of the site can be sold later. At domain auctions, interesting domains are sold at a very high price. If some well-known organization wants to buy a domain for their own use, then the benefit will be very great.
Advice: while there are not enough Cyrillic domains (those written in Russian), you can register a site name that is very promising for sale or development.