I'm sorry for any and all issues in syncing your laptop to the Messages + application. You mentioned that some of the contacts full names did not sync. What portion of the names did sync over? Are they missing first or last names, or does it show up differently for each one? Please clarify this for me, and we can get started.
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There are several discussions on this, one being Message+ Windows 10 App Alters Device Contact List. So far, no Verizon Support agents have been able to help. The Message+ desktop app is getting/creating its contact list in a way that apparently only the developers must know.
You can try editing the Contact(s) in the Verizon Cloud storage, but getting/keeping it sync'ed in the Message+ desktop app is the challenge. The Message+ desktop app creates a local SQL file which is what it uses for its contacts, but exactly where from and how it builds it or keeps it updated is the mystery.