There isn't anything that I know of that would alert 'joe pilot' to the fact that they are receiving a Doppler VOR rather than any other VOR.
Nothing on the charts, nothing in the approach plates, nothing in the chart supplement (old AF/D), etc....
When receiving, and tracking, the VOR signal - it should be steadier without so much of what is called 'roughness and scalloping' or 'bends' in the signal (basically what makes you feel like you are flying on a slalom course!) - it is just a 'cleaner' signal.
Also - the facility itself looks much different. Doppler VORs have numerous phase monitors situated all around the counterpoise/antenna whereas the conventional VOR has a few antenna monitors located around the counterpoise/antenna.
For example:
Panoramio - Photo of DIGITAL VOR (Doppler VOR) ground station, co-located with DME.(DETAILS COMMENT-8)
If you search Wiki for 'VHF omnidirectional range' there is some more detailed information and also pictures of Doppler VORs with many more phase monitors (1st and 2nd pictures of the facilities) and a conventional VOR with antenna monitors (the 3rd picture of a facility).
https://en.wikipedia.org/wiki/VHF_omnidirectional_range
In my opinion - if they want this 'MON' idea to work - they will be refurbishing MANY of the conventional VOR facilities over to Doppler - or they will not be able to achieve the increased service volume that they are hoping for in the future.
In short though Block30 - no sure of knowing when you are flying around which type you have tuned.