Why do names not show up on ipad messages

If the names aren't in your contacts on iPad that's why the messages aren't showing the name of the sender.

Try this:

On iPhone go to Settings > Apple ID, iCloud, iTunes and App Store

Tap iCloud

Make sure Contacts is Turned on in the Cloud

Now, do the very same thing on your iPad

This will permit your contacts to sync between the two devices.

OK......let's try a simple reboot:

If your iPad has a home button, press and hold BOTH the power and home buttons at the Same time until the Apple Logo appears (keep holding past the swipe to shut down), then let go and your iPad will reboot.

If you have a 2018 iPad Pro, without a home button, press and quickly release the volume up button, then press and quickly release the volume down button, the press and hold BOTH power and volume up buttons at the SAME time until the Apple Logo appears (again, holding past the swipe to shut down).

Are the people you've received these messages from in your contacts on your iPad?

In Settings > Messages > Send and Receive do you have your number AND email address checked?

Don't know what else to recommend. Either call Apple at 1-800-MY-APPLE or schedule an appointment at your Apple Store Genius Bar. Take both iPhone and iPad with you if you go in person.

Try this. Make any small edit to one of the contacts on your iPad. Maybe enter a fake phone number as an additional phone number. Save the edit. You can always remove it afterward. Close messages completely.

After you make the edit, and then get another text, see if the contact names start appearing.