If you don't like the previous domain, you can always register a new one and redirect the old one. Just check first if the new name is free. If not - choose another one, if so - order it. Then you need to transfer the site to a new address, correctly configuring the redirection from the old URL. This is done in order to notify the search engines about the domain name change.
Importantly! Before buying a new domain, be sure to check its history. It is possible that a site that had a bad reputation in Google/Yandex used to work under this address. It is better to refuse such a domain, as it will make it difficult to promote the site in search engines in the future.