If you have not yet done so, then it update your iPhone to the latest software version (currently iOS 11.1.1):
Update the iOS on your iPhone, iPad, or iPod touch - Apple Support
Messages can only be sent via iMessage when the recipient is using a compatible device and subject to connectivity:
About iMessage and SMS/MMS - Apple Support
It may help to follow the instructions here, including under the heading "Get help if you can't send or receive messages" and including unpairing and re-pairing your Apple Watch if necessary:
Read and reply to messages with your Apple Watch - Apple Support
The following steps may also help:
On your iPhone, in the Contacts app, check that there is a single contact card for each of your contacts and that each card contains that contact's full name and phone number, along with their email address.
If you have not yet done so, enable iCloud Contacts:
- On your iPhone, tap Settings > [your name] > iCloud > enable Contacts.
If you have contacts from multiple sources and multiple entries for the same person have not been linked automatically (such that they are shown as a unified contact, with "Unified Info"), then manually link those contacts by following the instructions here:
Delete prior Messages conversations with the affected contacts on each device:
- Messages conversations need to be deleted separately on your iPhone and Apple Watch.
- On each device, to delete a conversation: when viewing the list of conversations in Messages, swipe left on a conversation and confirm to delete it.
Having made any changes in the Contacts app, on your iPhone, in the Watch app, go to: My Watch > General > Reset > tap again on Reset Sync Data.
- Nothing will seem to happen, but the process will run in the background / invisibly to you, so allow some time afterwards for it to complete.
If the issue persists, it may then help to restart both your iPhone and your Apple Watch again, turning both off together, then restarting your iPhone first: