The expression "RNAV" began life with the meaning
Random
NAVigation. The idea was that the system was capable of navigation on random tracks. This concept was fairly short-lived because of the confusion that the term generated among pilots and ATCOs. Thus, the expression was modified to mean "Area Navigation", but I'm not sure that this is a real improvement...
Anyway, RNAV can be either VOR/DME or DME/DME. If it is based on VOR/DME, you must only use the specified VOR/DME and, indeed, your self-contained nav system - IRS or GPS - will do just that. If the chart allows DME/DME, the nav system will use all the DME facilitiesit can find. This can be a bit of a problem to the person designing the procedure as the system is quite capable of picking a DME that it beyond reception range or, worse, outside of a viable angle with the track.
Anyway, whichever system the procedure is designed to use will be shown on the chart. I suspect that most RNAV procedures are VOR/DME rather than DME/DME, due to the above problem. I have an idea that RNAV can also be construed as GNSS so that you only need to use a TSO 129A/145A/146A GPS Receiver, but I could stand to be corrected about that.
In any event, I'd be very surprised if the nav system installed in a late-ish model 737 can't handle RNAV.