There is one location within GetThru.app that an account's 10DLC information is viewable. It is in the ThruText dropdown under Account Tools > Brand & Use Case Registration.
Update March 10th, 2023: See this guide for information about the website URL prompt. This is a new requirement: Phone carriers are now vetting Use Case registrations manually. This change adds a new layer of verification with a higher bar for approval.
When filling out Brand Registration for the first time, see this guide: Adding Brand & Use Case Registration Information for 10DLC
For information about Use Case registration, see this guide: Use Case Registration
There are several parts to use case registration