This is not completely correct. Allah is a name as much as it is a "type". One of the things Arabs will point out is that Allah is "special" because it cannot be pluralized and hence is a better name for the monotheistic God than English God or Persian Khuda (which can be).
I'm a non-arabic speaking Muslim who prefers in non-liturgical context to use Khuda and have occasionally been "corrected" by well meaning folk.