Yes, you can import the HubSpot Owner for your HubSpot contacts by including the owner's first and last name or email address in your import .csv or, if your portal is integrated with Salesforce, the Salesforce Lead and Contact Owners.
To see the users that are available for use with the HubSpot Owner field, navigate to the Account tab (with your avatar image) > Settings > Users. If you want to add a HubSpot Owner, but they are not listed as a HubSpot user (and you are not integrated with Salesforce) you must add a new user.
If your HubSpot portal is integrated with Salesforce, the HubSpot Owner field will be populated with the Owner value for your Salesforce Leads and Contacts. If you were to import a value for HubSpot Owner that differs from a linked owner set in Salesforce, the next time that contact syncs (which will happen after the import, because there are changes to the record in HubSpot) the Owner value from HubSpot will override the value in Salesforce. Linking Salesforce Owners to HubSpot will happen automatically, as long as, the Email Address and Name match HubSpot Owners. If the Owners are not linked, then the Owner changes will revert upon a sync with Salesforce to the original value.
After reviewing the email addresses available for you HubSpot Owner contact property, update your .csv file to include a column for HubSpot Owner and add the user's email address or first and last name for each contact. For more information on importing contacts, check out this article.