Everyone housed in home, one with a name and in classical style (9)
I believe the answer is:
palladian
'in classical style' is the definition.
'everyone housed in home one with a name' is the wordplay.
'everyone' becomes 'all' (I've seen this before).
'housed in' indicates putting letters inside.
'home' becomes 'pad' (I've seen this before).
'one with' means one lot of letters go next to another.
'a name' becomes 'ian' (**).
'all' put into 'pad' is 'pallad'.
'pallad'+'ian'='PALLADIAN'
'and' acts as a link.
(Another definition for palladian that I've seen is " Neoclassical architectural style".)