Is there a way to show a 15+ character computer name in AD tools?

Sorry to say, you're going to have to shorten your naming convention. The maximum length of a computer name in Windows is 15 characters, and there is no way around that.

This is because the maximum length of a netBIOS account name is 16 characters - you can see this on page 10 of the RFC for NetBIOS.

Windows adds a dollar sign $ to the end of a computer account name to distinguish user accounts from computer accounts, which uses up one character, leaving 15 characters as the maximum length of a computer name.

Although you can create a computer object in Active Directory that's longer than 15 characters, the account name of that object will be only the first 15 characters, and that's why the AD tools only shows that many.