I'm Miles from the Social Care team at Shopify. I can appreciate the hesitation around the review process - especially if you've had your store open for 2 years. I want to stress; asking you to verify documents doesn't mean you've done anything wrong. It's simply a review that we complete on all merchants at any given time. This is covered in the Shopify Payments terms, which I'll go into detail about a bit later.
If your drivers' license doesn't match our records, it might just be the information was entered incorrectly at the time of setup, or something has been mixed up. If you've received emails from us around your payments being put on hold, I'd recommend replying to those emails directly. The team who manages those emails is best placed to help out with questions, as our general support team will only be able to create a ticket for them to contact you. So to save time, reply directly to those emails. If you haven't received any emails at all, then you will need to contact our support team for assistance.
In regards to the reason we ask for identity documents, I'd recommend having a read of the Shopify Payments Terms of Service. Section B part 3 explains the verification process for you. Here's a small excerpt from the terms:
To verify your identity, we may require additional information, including your company registration number or business number, your HST, GST, or tax number, and, if applicable, your date of birth. We may also ask for additional information to help verify your identity and assess your business risk, including, but not limited, to business invoices, reseller authorization or distributor information, a driver’s license or other government issued identification, or business license, for you or for any of the owners or principals of your business.
This explains what we may ask for and advises the reason for this is to verify for your identity and assess your business risk. If you require further clarity around the Terms of Service, I'd recommend seeking legal counsel.
I think it's great that you've used Shopify for two years. I'd love to hear more about your business and how it's doing. If there's anything you're struggling with outside of the payment issues, please let me know and I'll be happy to guide you through.