The display name is the name that your users can see once they open your WhatsApp Business API account profile. It is similar to any name we assign for our WhatsApp Apps.
The Display Name should have a relationship with your business and should not violate the WhatsApp Commerce & Business policies. Check here for complete details. The display name should abide by all these rules otherwise the display name gets rejected.
Yes, you can change a Display name multiple times. Here's a guide to changing your WhatsApp Display Name.
Yes, the green tick is assigned with the same display name. Hence, it’s really important to choose the Display Name wisely. But you also get an option of proving an alternative name for the Green Tick.
Read- How to get Green Tick on WhatsApp
Yes, it can be specific to particular department(s) of the company such as Finance, Sales, Customer Support, etc.