Is there a standardised noise source symbol for circuit diagrams?
Many noise sources are best thought of as current noise, or voltage noise, and for those, just use a 'two circle' or 'single circle' current generator or voltage generator respectively, with an appropriate resistor if they have a finite impedance. When I've used a noise diode, I've used a diode symbol.

Putting a circle round a component is often quite a good hint that it's a 'bit more' than just a diode, or a voltage source.