Note: I am not a lawyer, and do not pretend to be one. I pretend to be a hobgoblin. Get real legal advise if you want to be sure.
The word is protected
Greyhawk appears to be a registered trademark of Wizards of the Coast, at least as of 2020.
The whole point of having a trademark - including an unregistered one that is indicated by TM instead of the ® for registered ones - is that others cannot use that mark for related services. To quote from Wikipedia:
The owner of a trademark may pursue legal action against trademark infringement.
And to explain what Trademark Infringement is:
Trademark infringement is a violation of the exclusive rights attached to a trademark without the authorization of the trademark owner or any licensees (provided that such authorization was within the scope of the licence). Infringement may occur when one party, the "infringer", uses a trademark which is identical or confusingly similar to a trademark owned by another party, especially in relation to products or services which are identical or similar to the products or services which the registration covers
So no, if you want to be safe, you should not just use a trademarked word in your website or service, especially if that website is related to role playing games; at least not without obtaining a license or written confirmation from the owner that it is OK to do so. Because for a third party, it may not be clear if you are affiliated or under license with them, or not, so it may be "confusingly similar".
That said, there are non-profit sites like Greyhawk Online that is using a logo that contains even a registererd trademark. There also is the Greyhawk Wiki, or this one. While I do not know if these sites have an agreement with WotC, it at least seems to be possible to get one, or there seems to be no active enforcement of the name against non-profit fan use.
