In 2018, the three Ukrainian domain zones have opened a registration for emoji domains. In domain zones .BIZ.UA, .CO.UA and even with the free .PP.UA it became possible to use not only letters and numbers, but also pictures. As an example - i❤.biz.ua.
There are no special conditions or increased cost when registering: you just need to select emojis that meet the Unicode 11 standard (you can find a list of them on the official website) and check if such a domain is free.
After that the registration process is no different from the usual, non-emoji domain.
⚠️ Please note: in the address bar of most browsers the domain name will be automatically translated to Punycode, a special encode for domain names with Unicode characters. But in Safari's address bar you can see the domain with an emoji.