Bitly links are case sensitive. This means if your link is “bit.ly/CustomWord," then “bit.ly/customword” will lead to an error page or to a different destination.
You can make both work, however, if you edit your link to the other options. This is because when you edit a link, the older versions of that link still work. So, if you need to, edit your all-caps link to be lowercase, or to any other variations you think your audience might type in.
Editing your link combines metrics for all versions of the link, and they will all direct to the same initial long URL.