Classical liberals should take care to avoid some bad habits in usage.
Never use 'public' to denote 'government', or 'private' to denote 'non-government'.
Thus it should always be,
'government school' not 'public school',
'government transport' not 'public transport',
'government funding' not 'public funding',
'government policy' and never 'public policy'!
What to do with 'private company' and 'public company'? I think 'personal company' would do for 'private company'. A 'public company' is obviously not describable as a 'government company'. I can't think of anything better than 'open company', but 'universal company' might be better.
'Public' in fact is an unhelpful word, generally, as it is obscure in its reference, and is used to fig-leaf state involvement. Doesn't 'public library' sound better than 'government library'? Would you like to take a dip in the 'government pool'?
'Community' is a useful substitute for public. 'Community opinion' can do for 'public opinion', and 'community transport' for 'public transport' which is not solely a government enterprise. And 'community corporation' would be better than 'public corporation' in referring to a corporate body genuinely independent of the state. Similarly, 'community library' and 'community pool'.One might use 'community good' for 'public good', but 'universal good' is perhaps still better.