Any HubSpot account users with access to contacts can be designated as contact owners using the HubSpot Owner contact property.
To add a new HubSpot Owner:
If your HubSpot account is integrated with Salesforce, the HubSpot Owner property will be populated with the Owner value for your Salesforce Leads and Contacts. For more information on this, check out this article.
Please note that you can manually add additional users to a contact by creating a custom HubSpot user field type property. Instructions can be found here.