Hi,
In Messages > Preferences > Accounts > iMessages account you should see the Apple ID your are logged in with.
Below that is a List of the Receive At IDs that are linked if you also added that ID to other devices such as an iPhone or iPad.
Below that is the "Start Conversations from" drop down. This only appears if you use other IDs such as the iPhone Number in the Receive At list.
If you added your Apple ID to an iPhone and want the Mac to also show up on the Contacts' end then you will need to deselect the Apple ID as the Start Conversation From ID.
Repeat this on the iPhone Settings > Messages > Send and Receive.
I have my Mac set to Start Conversations From the Apple ID.
My iPhone is set to the iPhone Number.
As both Sync as both Sent and Received Messages on each devices window then a little info message in small grey text will appears like the Date Stamps do telling the ID has changed.
The mots common reason if you are testing with your self like this is if you send a new messages from the iPhone when the last one was from the Apple ID from the Mac end.
8:30 pm Saturday; January 9, 2016
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad