It can be down to the installation quite often. There are three potential sources of noise that that annoy I think.
(This is based on Eberspacher and Clones, but the Webasto works same way so the areas of issue are the same I would think)
1) Combustion Inlet and Outlet - External
2) Fuel Pump
3) Fan and Heater 'roar' (I don't know the correct term) - Internal
For 1), Silencers are essential otherwise it can be very annoying - and mostly to the people around you if you are on a campsite. What many don't realise is that a silencer on the INLET as well as the Outlet makes a fair difference as well. Given the low cost of the silencers, fitting these really is in the "no brainer" class of improvements.
A well-respected member of the "motorhomer" forum family swears by fitting two silencers in series for maximum effect. I did try this on mine and whilst the first one definately make a big difference, the second one didn't really do much more on mine, but maybe it might on another installation?
For 2), The constant 'tick, tick, tick' of the pulse pump when the heater is running can be an annoyance. My pump is outside and I can hear the pump ticking more than the exhaust when I am inside and there is no other sounds around. The pump jerks on each pulse and that can send a vibration and make the noise worse, so a damped mounting for the pump is essential. Advice on this excellent site about Eberspacher Heaters (
https://www.letonkinoisvarnish.co.uk/eberspacher_intro_1.html) suggests making the fuel pipe inlet and exit to the pump sit at a 90 degree angle to cut down on the noise.
For 3), a Heater with a fan makes a noise! I don't think my Chinese Clone of the Eberspacher, or the Eberspacher I have also had is any noiser in that respect than an electric fan heater. Personally I cannot sleep when I hear the constant ticking of a clock, but the heater when running is such a constant background noise I tend to tune out of it. Plus the heaters are so powerful for the size of room (inside of a camper) they are in, they are unlikely to be want to be running for that long overnight unless very cold!
Fitting externally would definately make it quieter, but you would still get some noise.
I was at the Motorhomer Kelso meet yesterday evening and had my heater running for a couple of hours until I left. It might be worth anyone who was there and near my van commenting if they noticed it and the level of noise/annoyance? When outside it could be heard, but I don't think it was bad, but maybe others might?
(if you did fit the heater underneath, it would help the occupant but could make your camping neighbours more annoyed if with others!)