There are two separate and distinct concepts around Verification and Vetting as applied to 10DLC messaging:
When you first register your Brand you're asked to submit the Brand name, tax ID, company address and contact details. After you complete this, your Brand will either be in a Verified state or and Unverified state. If you are in an Unverified state, you will not be able to run on 10DLC. This means there is information in your Brand registration that does not match your tax filing, thus the Brand cannot be verified. I must stress, your information must match your tax filing, or you will not get into a Verified state.
Important Notes:
This is a step where, as you register your Brand, you can also "Vet" the Brand in order to potentially increase the number of messages you can send on a daily basis. CSP's can apply for vetting on behalf of the Brand through one of the external vetting partners to gain access to Special Use cases or improve quality of service (where applicable). External vetting can be imported or carried out on the “Brand Details” page in TCR. You do not need to go through vetting, if you don't need high throughput. Standard vetting is basically a credit check. Enhanced vetting is a more detailed investigation into the Brand and may, or may not, increase your vetting score.