Hey sfromgi!
This may or may not be a solution, but I’ve had luck changing the name of my Mac in System Preferences > Sharing, (You’ll see your Mac’s name on top, and can change it there).
Next, restart both devices, the go into your iPhone Settings > Messages > Text Message Forwarding. From there turn off the old Mac name and then turn on the new name of your Mac.
You May get a message on your Mac telling you someone is signing into iMessage with your account, if this was what you just did, you should be able to allow it!
In similar issues with Bluetooth and cellular, I’ve had luck also changing the name of the iPhone in Settings > General > About.
And first off, on BOTH devices, you’ll want to make sure you show the same iMessage settings:
For iPhone:
Settings > Messages > Send and Receive.
For Mac > Messages > Preferences > iCloud/iMessage.
Hope something here helps!
How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support
If you can't send or receive messages on your iPhone, iPad, or iPod touch - Apple Support