How to determine Salesforce instance from Organization Id reported in unhandled exception email?

I am still not sure about the question. Do you have multiple Salesforce instances on a single email location?

Or are you owner of a managed package app that sends these mails based on error encountered by the app installer?

In both case the best way first is to document everything. There are many tools to keep track of your org ID and user id.

There is also License Management App that you can use to keep track of what is installed where.