Hi,
The one I found when I checked was when I had "called" my iPhone from my Mac.
My Mac is set to use the Apple ID to start new Messages from.
The iPhone is set to use the iPhone Number.
Also the "To" spot will not show you your My Card details (since El Capitan) as you are not expected to call yourself so to speak and you have to manually enter the number.
So in may case the Number is not directly (if that is the right word) linked to a Name.
However in the Chat window I and both Sender and Receiver and the Mac will see iMessages Sent to the iPhone Number and therefore it does seem to then recognise it is your details and put your Name in the "To" Spot.
Another possible is they are SMS. The one I found and checked and double clicked to open opened in separate window and it was all an SMS chat.
It also seems that chat was to my iPhone and it is "missing" from the conversation that contains iMessages to the same Number.

8:23 pm Friday; March 24, 2017
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone 6 iOS 10.x and an iPad (2)