First, import the deduplicated Account records. Then, if Account Name is marked as unique, you could import your prepared Contact data and import to the Account lookup field matching on Account Name. Otherwise, you’d need to export Accounts and then run a VLOOKUP between those and your Contacts (matching on Account Name) in order to grab the Account ID.
Basically, marking Account Name as a unique field in your CRM is a GREAT IDEA.
Before import, think about setting up assignment rules if you have more than one user. You can set those up in the CRM, or, if you have specific assignments that can’t be automated, you actually need to indicate with an ‘Owner ID’ column and import the specific assignments to the corresponding field.