Yes, you can use very completely unique domain names in the hive. And just to clarify, you want to point domain1.com and domain2.com to the same file folder in your server, not pointing one to the other.
You are in the right area of CPanel - Addon domain, or a Parked domain. A parked domain forces you to use the same directory as the primary domain in the account, but the addon you can specify a subfolder to point it to. Generally you can use a parked domain if your WP files are in the root (/www, or /public_html) and use an addon domain if your WP files are in a subdirectory (/www/wordpress, or /public_html/wordpress)
Regarding the error you got from CPanel, it appears that that an entry for that domain name already exists on the server, and CPanel won't let you use it. That is an issue you'd have to take up with your web-host. If you do own the domain, then one thought is that it's possible you registered it on that server before using a different account.