We have a managed package that we don't want to publish to App Exchange. Is there any way that we can get our separate governor limits, so our operations wouldn't count against the installing organization limits?
Refer 'Per-Transaction Certified Managed Package Limits' section in https://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/apex_gov_limits.htm
Certified managed packages—managed packages that have passed the security review for AppExchange—get their own set of limits for most per-transaction limits. Certified managed packages are developed by Salesforce ISV Partners, are installed in your org from Salesforce AppExchange, and have unique namespaces.
Possible duplicate of https://developer.salesforce.com/forums/?id=906F00000008uIDIAY