macosmessages
On my mac I used to be able to send to other mobile devices from my iMessage but now it won't send to phone numbers. It sends to iMessages and emails but not non-iOS phone numbers.
I've tried to delete the iCloud account from my Mac and re-enable it.
I've also done the same on my phone.
Still getting the name highlighted in red
I'd try to Reset Network Settings, as detailed here: Not receiving Text Messages after upgrade to iOS 7 -- this seems to cure a wide range of ills for Messages.
It's an issue with OS X & Exchange sync. As a workaround, you can use the OWA app by Microsoft to sync your contacts to iCloud:
On iOS there's an app called OWA. Within the app there's a setting within the People section for sync'ing your contacts. Basically it creates a new group in your iCloud called OWA that is a carbon copy of your contacts.
Once I turned this on and saw it sync with my laptop, I got my names resolved and showing in iMessage again!
I have documented a more complete explanation and resolution in Resolving Contacts Sync on OS X - Error SOAPWebServicesErrorDomain.
Best Answer
Simple first-try fix for a 'red name' above the iMessage pane is click it & reselect the correct contact type/number/email - even if it's the same as the current top line, select it again from lower down the list.
Even if the number cannot accept 'blue' iMessages, it will make the system try again.
Also -
Make sure you have turned on Text Message Forwarding in the Messages settings on your phone. A reset may disable this.
For further options, try https://support.apple.com/en-us/HT204270
or http://www.macrumors.com/2014/11/06/text-messages-phone-calls-on-your-mac/