You can import a CSV file with multiple contacts associated to a single account or company name by adding a column for the Account Name and another column for related contacts in the CSV File.
If you import contacts using only the account or company name, and you don't have an existing account, then an account gets created with only the account name.
If you already have the accounts' information in the file, you can first import the accounts by mapping the fields related to that account and then import contacts by mapping the account name.
This will help you create contacts under the same Account or Company Name.