Integrate AD with local SQL Server

Question

I have a local SQL Server. My computer login is Domain\myName.

The local SQL Server instance allows me to sign in using Windows authentication. I am in logins as Domain\myName. I am using a third party app that creates a directory that only Domain\myName can access.

So I tried to create a credential for Domain\myName and then use a proxy to run a SQL Server Agent job that writes to that directory. However, when I right click on credentials, the only location that show up is <mycomputername>, so Domain\myName does not appear in the identity list.

How can I get Domain\myName to be able to run a job with the correct authorization to write to a directory?

Thanks