It depends how demodulation is supposed to be done:
If in hardware one needs a square wave of the same frequency with suitable phase, possible two with a 90 deg phase shift. For a phase shift one might use an PLL, but with fixed frequency an other method might be easier.
The DDS chip might have an extra sync / square wave output, but not all DDS chips have one.
I doubt one would really need a pure sine for excitation - it might be easier to crate the drive signal from a filtered square wave. This would make is easier to derive the demodulation signal(s). The filter circuit could also be used for phase adjustment (if needed).
The alternative would be demodulation in software: using a faster ADC and doing it in math. This would also need a start signal, but one could use something like an µC do generate a square signal for the driving signal and read the ADC and do demodulation - so no external demodulation signal needed, it is just virtual in software.