The name "Romania" (România) was first brought to Paris by young Romanian intellectuals in the 1840s, where it was spelled "Roumanie" in order to differentiate Romanians from Romans. The French spelling version (Roumanie) spread to other countries.

In English, the name of the country was originally borrowed from French "Roumania" (<"Roumanie"), then evolved into "Rumania", but was eventually replaced after World War II by the name used officially: "Romania". Most other countries still spell it with a "u".

As to why English uses an "o", "ru" is a more unusual sound in English than "ro". Basically, we Anglicized it.