So, this problem has been plaguing for about 2 weeks now, I have a Samsung Galaxy Note 20 Ultra and Windows 10 desktop and laptop. This has happened with the Phone Link app on the desktop only for whatever reason. One solution I had several weeks ago for one contact only which began showing up as a cell phone number rather than name, was to delete the contact on my phone and re-enter it. For whatever reason, that fixed it.
Now, this just started happening with whoever is in my list of Samsung messages on the Phone Link app on my PC. No way was I deleting all those people and re-entering.
My temporary solution which again just worked tonight, as it is flaky, works for a few days and then reverts back: I go into the Link to Windows app on my phone, and at the bottom of the app it says SYNC CONTACTS, which is supposed to sync the Microsoft contacts on all devices and apps. I am not questioning this! After a T-Mobile update last week, for whatever reason, the SYNC CONTACTS was disabled. Turning it back on and voila! The contacts names were listed again on the Phone Link app. Now, this has been happening every few days since then including tonight. Even though the SYNC CONTACTS IS enabled on the Link to Windows app on the Samsung phone, I disable it and then re-enable it and the contacts names return as it just did now. It's annoying. I never had to do this before. But it's way easier than having to re-enter contacts names or add "other" phone number. And to the OP, yes, the numbers when they appear have a 1+999-999-9999 format.