Are you worried about domain ownership, or copyright protection?
The domain is theirs unless you can buy it from them. Nothing you can really do about that.
If you're in the US, copyright protection issues are a whole separate issue, and domain name availability doesn't have much to do with it. What maters is the use of the business name, not the existence of a website. If there is already a business in a related industry and potentially serving the same market, you'll need to find a different name. If it's not clear whether there is, you'll need a copyright lawyer.
A gym in a neighboring state opened a BJJ gym with the same name as mine, and was pretty shady. I didn't want to be associated with them by mistake. It wasn't worth pursuing legally (and I would likely not have won, since we're brick-and-mortar businesses in different states), so I just changed our name. I did some research and found that another gym already had my preferred name, so I modified it slightly. However, all of the domains for that modified name were taken by unrelated businesses. So I found a completely different name that wasn't being used by anyone in the martial arts and had URL and social media availability. It wasn't my first choice, but it was the best I could do. You've just gotta be willing to compromise
These days, finding a suitable available URL (and probably social media usernames) should be part of the naming process, and you should purchase the domain before you actually make the website. You should also buy up similar domains to prevent this same situation. You don't just want to own goldengrappling.com, but also goldengrappling.net, golden-grappling.com, etc.
Also, I do hope that "Golden Grappling" is just an example you're using, and not the actual name.
