I'm sorry. My original reply did not post.
I've been told that customer account numbers or IDs exist. However I have not been able to view or display them.
Quick scenario summary. We exported about 7k customers from old software A to new software B. Since software A never synced with QB it did not matter if customer names did not match exactly. Now we are preparing to sync software B with QB and need the customer names to match exactly. Software B is requesting our QB company file in order to match customers and clean up the many that do not. For this they require a specific identifier (Customer acct #/QB ID) as opposed to matching a John Doe with a Johnathan Doe by address or phone/email.
My company is hesitant to share our company file, so I was hoping to create an export with Customer Account #/QB ID, Customer Name, Address, Phone, Email. I just need to find a way to find and include the customer #/QB ID part.
OK, that makes sense.
There is no visible unique number assigned to customers by QuickBooks. There is the Account # field, where you can enter nothing or any text you want, and it can be a duplicated on different customers. So, neither required nor unique.
However, there is a ID assigned to each name as it's created - which will never change for that name. You can't see it within QuickBooks, but you can see it if you export the customers to an IIF file, which is a tab-delimited file you can open in Excel. The IDs are in the REFNUM column:

All of the other data fields you mentioned are in the IIF file as well.