Are push notifications connected to my phone number?

No.

Push notifications operate independently of your phone number, though they do require an internet connection.

This means you can receive Zucoin transfer notifications even if your phone number changes, as long as you have enabled notifications in the Zucoin wallet app and have an active internet connection.

More on this topic:

How do I turn on push notifications?

My push notifications are not coming through. What can I do?

Zucoin releases mega update, one-tap notifications, sub-second transaction speeds