Can I buy a same domain name with different TLD and add similar content with different design of site? Is there any copyright issue?
to be more precise, imagine site which have function ''remove bg from photo'' and domain ''hidebg.com'' if I buy domain ''hidebg.org'' and add different design with same function remove bg from photo with some extra function like convert photo to different formats, thats legal?
There are two areas of law that are relevant here: Copyright and Trademarks.
Copyright is only a problem when the content or design is copied verbatim or a derivative work. Just being similar in nature is (usually) not enough for a copyright claim. Specifically, copyright doesn't apply to abstract ideas or methods. So creating a product that has the same functionality as a product from someone else is usually not a copyright violation as long as it was developed independently (patents might sometimes apply here, but that's a whole other can of worms).
But the bigger problem here might be trademarks. Trademark law says that you are not allowed to sell goods and/or services under a name (or a confusingly similar name) as a competitor offering goods and services in the same category. Trademarks can be registered to obtain stronger legal protection, and a well-organized and well-funded company will usually do so. But one can also gain so-called "common law" or "unregistered" trademark protection by simply using a name in commerce. Using a domain that is similar to a trademark owned by someone else can be legally problematic, especially when they are in the same industry. See the well-documented landmark case from 20 years ago Microsoft vs. MikeRoweSoft. Yes, Microsoft settled in this case, but they were forced to do so by the court of public opinion, not by the court of law.
But note that in many jurisdictions, trademark protection requires that one actually does business under that name. It often does not protect strictly non-commercial activity.
Another limitation on trademark protection is that it does not apply to "descriptive" or "generic" terms. When one sells a good/service under a name that literally describes the kind of good/service being sold (like in this case "hidebg" for a service that hides the background of an image) then a court may rule that the name is too generic to warrant protection. But this is an argument you (or rather your very well-paid trademark lawyer) would make in court. And there is no guarantee that the judge would see it the same way you do.
