Office 365 and Office (desktop) are one and the same. All that really matters is the license you're using. You didn't mention what version of Office you purchased but I'm assuming it is the latest version.
In that case open any Office app and go to Account
. Under Product Information click the Switch License option and it should walk you through hooking up your account to Office. Then you're done. Note that Office switched a while back to tying Office to your MS account so if you switch to your MS account then it should automatically pick up the license. I'm assuming here you're not using a product key.
After you switch licenses/accounts then restart Office and you're now using the correct account. Nothing in Office will change. Note that if your account doesn't have access to all the same software that the original one did (e.g. Access) then those apps will no longer work. Also note, as mentioned earlier, this is only applicable if you purchased a newer version of Office. If your license is for something old like Office 2016 then you would need to uninstall Office 365 first and then install the correct version of Office using your software media that you should have.