Since you've probably been using the SMB protocol to access the NAS you probably need to understand a few things about the NFS protocol which functions differently. The NFS mount acts like a mapping of the entire system, rather than a specific user. That means that if there are differences in the systems, you may get access errors. For example the default user in Synology has a uid of 1024, but most client systems have a default of 1000. This means your user may not have access to the share or files, even if you have it mounted on the client.
One thing to check is what your Shared Folder's NFS permissions squash is set to. This is found in Control Panel > Shared Folder the the NFS permissions tab. If it's set to "no mapping" then uids must match. The easiest setup is to "map all users to admin" but you may encounter issues with that later if you switch back to SMB since new files will be owned by admin.