iMessage Problem Syncing between iPhone and Mac

My texts messages that are sent on my phone are not syncing with my MacBook Pro. I tried logging out of iMessages on my phone and turning it off, turning it back on and logging back in, but it's still not syncing. Also on my MacBook Pro under iMessages it only shows the phone numbers of people I've sent text to and not their names like it does on my phone. Some of the phone numbers in iMessage on my MacBook Pro are also red. Why is this?

I'm still running OS X Yosemite 10.10.5 and haven't updated to El Capitan because I wasn't sure if the update was having issues with Microsoft Word still.