This depends on the type of business and clients. Normally, the Customer Center is setup in a hierarchical way. If it does not look like this in your QuickBooks, then go to the Customer list and right click. In the drop down menu there should be an option for "Hierarchy view", so it will look like my example below:
Client Company Name
For instance, if you have a contracting company, then you would use this method to keep track of different contracts. I would not suggest you use the contract number, but instead set up a job number and make sure the naming convention makes sense. For example, lets say you won a contract with Wyzant today, October 10, 2019, then in the area that says "contract name" above you could write "191010-01 Wyzant Contract". Normally you use the full date if the project is not going to be more than one day. If your projects normally are monthly, you should use "19100-01 Wyzant Contract". If projects are run annually or exceed a year, then you'd want to use "1900001 Wyzant Contract". As you probably noticed, the last two numbers were "01" but the idea is that you can just scale them from there until how ever number of contracts you have with that company. Of course the idea it that you'd make their contract/client company inactive if all the the invoices have been paid and you are no longer working with them.
Hope this helps!