To be able to get a .UA domain, you need to have a trademark. But the administrator of the domain zone has a number of requirements that you should be aware of.
The first and most importantly: it should be an Ukrainian trademark or or international, but with an extension for Ukraine (the Madrid Protocol). You can't use local trademarks of other countries, trademarks designated for EU or other country associations.
Second, to register domain "example.ua" you need a trademark, which image has the word "example" - and nothing more. If the image has other words - they must also be in the domain. As an example:
- with TM "Example®" you can get the domain exampleR.ua;
- with TM "Example Пример Приклад" you can get the domain Example-Prymer-Pryklad.ua (you can't just "throw out" the words from the TM).