I was able to fix this on my computer by following these steps:
- In the Phone Link app on PC, go to Settings, click the My Devices tab, and use the ellipsis (...) menu on your device to remove it, then close the app.
- On your phone (mine is an Android), go to Settings, Apps, Link to Windows, Open, then remove your PC from the Linked Computers section.
- Restart your phone.
- Re-link the phone and PC by restarting the Phone Link app on your PC and following the step to add your device.
- Perhaps this is the critical thing, but I noticed in the Link to Windows app on Android, there is a toggle to "Sync contacts" under the list of Linked Computers, which was disabled for me. Turn this on.
Contacts are showing up again for me now - yay!
I do not see a "Sync Contacts" toggle in the Link to Windows app under the list of Linked Computers. These are the only toggles I have under the list of Linked Computers:

I did notice that the Account in my Link to Windows settings is my Microsoft account (not surprising), but I'm pretty sure all my contacts are associated with other accounts (my Samsung account and Google accounts and my primary email account). Could that be why some of the contacts aren't synching? I don't use my Microsoft account much, and don't have contacts in it. But most of my contacts do show up as names in Phone Link, only a few of them, the most recently added ones, don't.