Absolutely. Plugging in a DAQ device tells LabVIEW/MAX not only the type of the device (e.g. "myDAQ"), but also its Serial Number. It wouldn't surprise me if plugging in myDAQ A, removing it, and plugging in myDAQ B would result in A and B having different "MAX Device Names".
I tend to let DAQmx find my devices. There's a function (somewhere) that will enumerate all of the DAQmx devices that are connected, and you can then have a For Loop that looks for "USB-6001", "USB-6002", "USB-6009" etc. (if those are the devices that work with your code). Once you find the right device, you can ask for its Serial Number (very handy when you build the device "inside of" a larger chassis that has Power Supplies, local circuitry, etc. (so that you know "it's the myDAQdevice that is wired into my myGadget").
The other time I used this "trick" was with Video (which, fortunately, I'm not doing right now). It was not unusual for me to have several cameras (including the one inside the Laptop, plus a WebCam, plus an Axis camera over TCP/IP) -- the code was written to say "No Camera" (if there were no Cameras detected), choose the "only" Camera (if there was exactly one found), or present me with a list and say "Which do you want to use?". Same idea, let LabVIEW help you understand what devices are connected, and let you choose what to use.
Bob Schor
