Yes, you can set ownership for your HubSpot records by including the owner's first and last name or email address in your import .csv.
To see the users that are available for use in your HubSpot Owner or custom owner properties, navigate to the Account menu (top right corner next to your avatar) > Settings > Users. If the owner is not listed, you must add a new user (unless you're integrated with Salesforce; see below).
After reviewing the users in your account, update your import file to include a column for HubSpot Owner or your custom owner property. Add the user's first and last name or email address for each corresponding contact. For more information on importing contacts, check out this article.
If your HubSpot account is integrated with Salesforce, the HubSpot Owner property will automatically be populated with the Owner value for your Salesforce Leads and Contacts. If you were to import a HubSpot Owner that differs from the owner set in Salesforce, the value from HubSpot will override the value in Salesforce when the contact syncs. When you create a new user in HubSpot, HubSpot will automatically match them to the corresponding Owner in Salesforce as long as the name and email address are the same.