Permission problems with Windows 10 Pro - ReadyNAS 2120 v2 - Office 365

It sounds like you are using Microsoft accounts, and not local accounts. I don't think you can get Microsoft logins to work.  But you can specify different user credentials for the NAS in the windows credential manager.

It makes sense to start by deleting any credentials that are already in the windows credential manager. 

After that, try creating a single user account in the NAS.  The user account shouldn't match the name of any of the PCs accessing the NAS, and it also can't match any share name.

Then you can test access using that account using CMD in the windows system:

net use * /delete /y
net use t: \\nas-name\sharename /user:username userpassword

using the real nas-name, user name, and user password (and of course a real share).  Be careful on the typing - particularly the two slash directions.

The first command terminates any open SMB sessions in the PC; the second attempts to map the share to drive letter T.

Once you've confirmed that works, you can enter a windows credential in the Windows credential manager for the NAS (specifying that username and (optionally) the password).

Note you can use a single (shared) NAS account on all the PCs if you like (though that assumes that you don't need the private folder feature, and also that you don't need to restrict access to some shares).