I'd like that less. The point for me is to remove duplication and unneccesary information so I can quickly see the problem. In almost all contexts I can either see the associated device which assumedly has the name "Server" or I can edit the template such that the device name always precedes the sensor name resulting in "Server Ping 382". Also, for easy recognition, a hierarchy of information is important. Start with Probe name to ID the site the problem is at, the device to narrow it from there and then the sensor to pinpoint the problem. Perhaps "sensor device" is fine on smaller implementations, but we have 30+ probes with nearly 4000 sensors and growing. Keeping track of that means the flexibility of being intentional. I'm still renaming probes all the time to remove the number as at that level of sensors, no one is remembering which ping sensor is number 543.
On small phone screens when we have someone on call, extra info is really obnoxious as it obscures the useful info. Let me KISS it by giving me the flexibility to set this up as I want without numbers and I'll be very grateful. Adding the device name into the sensor name would be counterproductive for my implementation.