I have this same exact question too and the answer provide no help what so ever. I have recent contacts (some have been deleted for over a year) and they are coming up only when I use iMessage on my Macbook. When I use iMessage on my iPhone they do not pop up at all. This has to be the most frustrating thing ever and makes me not want to use iMessage on my Macbook at all. The suggestion at the bottom says you delete them from contacts and they wont show up anymore couldn't be more wrong. THEY ARE DELETED FROM MY CONTACTS and they still show up on my iMessage app. I have texted people on my macbook multiple times that I DO NOT WANT TO TEXT. I am a coach and I had a lot of old coaches listed as coach... then their names. Well some have similar names that I have deleted and no longer talk to and when i type in coach their names still appear and I have accidentally clicked on them. Some of them had the same name and the contact looked the same with different numbers I realize that this was a bad move by me but I didn't think I could have this problem. But then I started texting someone who I thought was someone else and it has be SO CONFUSING. I hate this about apple, and then there is no way to fix the the problem.
Bottom line I have old DELETED contacts (YES THEY ARE DELETED OFF MY CONTACTS) showing up on my Macbook iMessage when I start typing their name. And yes I have gone on my iPhone and hit the i and removed these contacts ages ago and they no longer show up on recents on the iPhone. I have no clue on what to do, doubt I'll get help here though.