Can a theme use two URLs at the same time?

After the purchased theme was used as a test site, all the data of the test site has been deleted and removed. Can I continue to use this theme if I build a new website? If it can be used, do I need to unbind the domain name or IP?

In most cases, localhost or “Staging” domain/websites are allowed but if you have registered the theme already, yes, you’d need to switch the domain. Check the documentation of the theme and contact the item author for more information.