Pedantic nitpick: you are most likely talking about a different 'colour' of noise. White noise is really harsh, and probably not what your fan produces.

See https://en.wikipedia.org/wiki/Colors_of_noise

I couldn't remember the color (brown noise?) so white noise was the best thing I could come up with.

No worries. When speaking colloquially, 'white noise' is a perfectly fine term and perfectly understandable.

yes, but that wasn't white noise I assure you :-D

Especially if there was classic IDE HDD grinding involved :D

I've had 24x7 FIDO node in my room for years. I've silenced modem pulse dialing by replacing relay with expensive one. I've silenced CPU cooler by using 90mm 12v fans connected to 5v (yes, in 486DX era). But HDD was unbeatable.

On the other hand, if I wake up in the middle of the night due to HDD grinding, I was sure that I have new mail (echoareas) to read!

I loved that deep scratchy bass, modern hard drives are so quiet... I miss sleeping to my computer defragging all night long :(

Not all modern drives. One of mine goes "thunk thunk thunk". I could hear it from rooms away in one case I had it in.