If you're editing the back-half of a link and see the error This custom link is taken, you'll need to enter a different back-half. This is because someone has already used that back-half with that domain, whether it's bit.ly or your own custom domain.
Since Bitly links are case sensitive, try changing the capitalization. You can also add other characters, like numbers or a hyphen.
For example, if someone has used yourdomain.com/sample, and you wanted to use the sample back-half, you could try yourdomain.com/Sample or yourdomain.com/sample2022.
Think strategically when customizing your links. When you add a custom back-half to a link, it is permanently tied to that link. It cannot be freed up later, even if you go back and edit the custom link in your account.