You can verify the timing source in the ATLAS by looking under SYSTEM STATUS at the "System Timing Source." It should show either "PRIMARY : Locked" or "BACKUP : Locked." If this is toggling between PRIMARY and BACKUP then you should set both PRIMARY and BACKUP to INTERNAL and see if the ATLAS can lock on to the internal clock. If it cannot then the ATLAS needs to be sent in for repair. If the timing source shows "BACKUP : Locked" then the ATLAS is not receiving a stable clock from the primary source.
Is the ATLAS PRI interface showing Controlled Slip Seconds (CSS) as well as Errored Seconds? If it is then those are clock slips, which means the data the ATLAS is receiving on that PRI is using a different clock then the clock the ATLAS is using. If it is only showing Errored Seconds then these are CRC errors and could be a bad cable. You can use a T1 Loopback Plug to loop the port on the ATLAS as well as the port on the PBX to see if both run clean to a loopback. If either runs errors to a loopback then that T1/PRI port is bad.
In order for the system name to change, someone would have to have typed in the new name. The default system name is "ATLAS 550" so it was not defaulted, and the word "CARRIER" does not appear anywhere in the ATLAS menus.
If your "secondary" PRI shows errors and clock-slips then that can cause calls to fail. If both PRIs are from the same telco then you should be able to set your PRIMARY clock to your "main" PRI and the BACKUP clock to the "secondary" PRI and they should both be using the same clock from the central office.
Hope this helps,