To set up your Synology as a Time Machine backup target for your Mac:
1. Go to Control Panel > File Services > Advanced.
2. Tick Enable Mac file service.
3. Choose a shared folder from the Time Machine drop-down menu.
That shared folder becomes Time Machine’s backup destination.
A related Synology KB also says to:
1. Sign in to DSM with an administrator account.
2. Go to Control Panel > Shared Folder and click Create.
3. Create a shared folder for Time Machine.
4. Synology does not recommend enabling the recycle bin feature or using encrypted shared folders as the Time Machine destination.
5. Finish the wizard, then select that folder as the backup target.
In the connection steps, on your Mac use Go > Connect to Server, enter the NAS IP address, connect with your credentials, select the shared folder, keep the Finder window open, then open System Preferences > Time Machine > Select Disk and choose that shared folder.
For Time Machine errors:
- Make sure your Mac is properly configured for Time Machine backups.
- Make sure your Mac has enough free space.
- Make sure your Mac and NAS are on the same local area network (LAN).
- Make sure your Mac is connected to your NAS via SMB3.
- If possible, connect your Mac to your NAS via a wired network connection.
- If needed, start up your Mac in safe mode and try the backup again.
If the error is “insufficient space”:
- Free up space on your Synology system or Mac, depending on the message.
- On the Synology system, make sure the storage pool and volume where the Time Machine folder is located show Healthy status.
- For DSM 6.x, check this in Storage Manager > Storage Pool or Volume.
- Make sure there is enough free space, and if you assigned a quota, check the remaining amount.
Sources used: [1], [9], [10], [11], [12]