I am almost certain I remember, although it may be a false memory, TMH mentioning that The Culture are called that because they didn't want a name; same reason they have no flag, capital planet or city, anthem, borders (The Culture doesn't end, it just fades away). No Ra Ra nationalism, no us for there to be a them, only we and future potential we.
If my memory is correct, then The Culture were given their name by others who were fed up of having to refer to them as 'that lot' or equivalent.
They didn't want a name... such a simple, straightforward yet positively badass thing to do.
Outside Context Problem (OCP), the kind of problem "most civilisations would encounter just once, and which they tended to encounter rather in the same way a sentence encountered a full stop."