You would need to add a new field to the customers table ...
Then customize the code for creating accounts and editing accounts ... depending on how this field gets in there ...
Then customize the Admin section for Customer ... Customers ... so you can edit view the data ...
Then need to customize the orders table if you need this code to carry over to the orders ...
Then customize the account history if you need the new field to show on the customer order ...
Then need to customize the orders, invoice and packing slip if you need it to show there ...
You have not given enough information about how you want to use this new field, where it shows and what you intend to do with it, if anything, beyond display ...