I am using the Import wizard.  Also importing using two templates:

One Template is for the Lead Record and contains:

Company Name = ENV00026 Name
Individual = FALSE
Status = Lead-Unqualified
Unsubscribe = No

Second Template for Contact:

Unsubsrive = No
Inactive = No
Customer ID = ENV00026 Name
Contact = Full Contact Name
Last Name = Last Name
Middle Name = Middle Name
First Name = First Name
Addressee = Addressee
Job Title = Job Title
Address 1 = Address 1
City= City
State = State
Zip = Zip
Phone = Phone
Email = Email

I am mapping the Company Name with the Company ID.

I have tried mapping Company ID with Company ID, Company Name with Company Name  and Company ID with Company Name.