Petend was likely the name of the town till about 130 years ago. In the late 19th century, the Hungarian Government carried out a major exercise in making a town's name unique over the entire kingdom. I guess that the prefix Zala was officially added at that time.
Petend was the seat of a Roman-catholic parish, the faith of most of the circa 450 inhabitants. LDS have microfilmed the parish records. Recently, an online index of all births has become available.
From October 1895, civil recording took over. I don't know where the people of Petend had their civil recording office. You could find out by checking all nearby towns for microfilms of civil records in the LDS Library. Spot-check these films for vital records of persons from Zalapetend, starting with the nearest such town.