Here is a checklist to go through. Note that the settings on the iPhone are as important as those on the iMac and ALL must show correctly, and note especially the one in bold below:
iMessage checklist
iPhone and Mac both logged in to same Apple ID. Try logging off and logging on if necessary.
iPhone Settings => Messages shows iMessage as "on" (sometimes toggling this off and then on fixes some things)
iPhone Settings => Messages shows Send & Receive showing both phone number and email (Apple ID)
iPhone Settings => Messages shows Text Message Forwarding and your Mac is listed and shown as "on" there.
iPhone Settings => Messages shows Send as SMS "on" and MMS Messaging and Group Messaging both "on"
On the Mac: Messages => Preferences shows same and correct Apple ID and "You can be reached for messages at" indicates both phone number and Apple ID (email), and "start new conversations from" indicates the phone number.
* Don't see the Text Message Forwarding setting on your iPhone? Go to Settings > Messages, turn off iMessage, turn it back on, tap Send & Receive, tap Use Your Apple ID for iMessage, then sign in with the same Apple ID used on your other devices.
Forward SMS/MMS text messages from your iPhone to your Mac or iPad - Apple Support