The Church called itself both Catholic and Orthodox in the 1st millenium. "Catholic" was the first common term, understood in the sense of "according to the whole" - every local Church is the whole Church, because Christ is present, sacramentally through the Eucharist and symbolically through the bishop. Later on, "Catholic" caught on in the West (but understood in the sense of "universal", referring to the Church's mission of universal evangelization which is being fulfilled more and more everyday) and "Orthodox" caught in the East ("proper faith/worship", in opposition to heretical sects, especially the Monophysites).
Today the Eastern Orthodox Church officially refers to itself as the "Orthodox Catholic Church" or as the "Eastern Catholic Church". And while the title of "Orthodox" isn't really used in the West anymore, most Eastern Catholic churches call themselves "Orthodox" liturgically. To add to this mess, the Monophysites have decided to call themselves "Oriental Orthodox" since the 1960's.
The title of "Western Orthodox" is unlikely to be used by the Catholics simply because 1) "universal" is already a traditional title and more relevant to the Pope's universal jurisdiction, 2) the title of "Catholic" understood in the Greek sense has been recovered with Vatican II (thanks to the influence of Nicholas Afanasiev), and 3) the Orthodox have called dibs on the "Western Orthodox" title, with their Western Rite.
>Hell, one of the titles of the Pope is "Patriarch of the West", first used by Pope Theodore I in 642.
The Pope took back this title in 1863… and dropped it again in 2006.