The answer to this question is a bit complicated. While Discord does have a feature that allows server owners to see who has generated invite links, it is not always accurate.
This is because people can change their usernames, and Discord does not keep track of IP addresses. So, if someone changes their username and then generates an invite link, the server owner will not be able to see who originally created the link.
However, if someone generates an invite link and then sends it to another person, the server owner will be able to see the second person’s username.
So, while server owners cannot always see who initially creates invite links, they can usually see who spreads them around. This can be useful for tracking down problematic users or for simply keeping an eye on who is sharing links to your server.
If you’re ever concerned about someone generating invite links to your server without your permission, you can always disable the feature in your server’s settings.
This will prevent anyone from creating invite links, and it will also prevent people from joining your server through invite links that were created before you disabled the feature.