"The early Italian house consisted only of the atrium and the surrounding rooms, with, in most cases, a small garden at the back.... Out of the small plot at the back of the early house developed the peristylium, a garden surrounded by colonnades on to which rooms opened on all sides,... The peristylium, both in general appearance and in name, reproduced the men's room of a Greek house. Whilst the names of the front rooms of a Roman house are Italian (sic) (atrium,fauces, alae, tablinum) those of the back are Greek (peristylium, triclinium, oecus, exhedra)"
Rome: It's people, life and customs, Ugo Enrico Paoli, 1940, trans. R. D. Macnaghten, English version 1958.
Comment and link incorporated as suggested by @Cerberus
This link discusses the House of the Surgeon and the architectural development mentioned :-
L&S give this as the derivation of peristylium :-
peristylium The Greek adjective περίστυλος is applied either to a court surrounded by colonnades on the inside, or to a building surrounded by them on the outside, as a temple. It is then used alone, in all three genders, with a substantive understood, for a court with colonnades: hence the Latin peristylum, or more commonly the substantive form peristylium. It is especially used for the courts of a Greek dwellinghouse, and for that introduced into Roman houses in imitation of them.