The change of the official town name from Petend to Zalapetend likely happened in the late 19th century. In 1938, Zalapetend was amalgamated with the neighboring town or village of Vigánt and the official name became Vigántpetend.
I don't know when the district of Tapolca (where Petend is located) moved from county Zala to county Vészprém.
The change to civil recording was a separate development. Since the reforms introduced by Joseph II (German emperor from 1780-1790), the churches were the official recorders and keepers of vital data like births, marriages and deaths. In the late 19th century, the Hungarian Government decided to introduce civil recording and relieve the religions of their official recording role. The switchover happened on October 1, 1895.
As per Joseph's message, civil recording for Zalapetend and for Vigánt were in Taliándörögd. If your ancestors were Roman-catholic as most inhabitants of Petend, you should examine the related microfilms of the parish of Petend (Zalapetend) which run till end of September 1895. The continuation are the civil records, also filmed by LDS, which cover all religions.
What Joseph tried to convey to you about the two other place names called Petend puszta in Zala county is to keep their existence in the back of your mind in case you would be unable to pick up a track to your ancestors in the records of Zalapetend. Pusztas are meadowland areas of scattered houses. If the source of your information says Petend in Zala county, there is a slight but real chance that it does not refer to Zalapetend, but to one of the places called Petend puszta.
It happened in my own search for the birth record of my Hungarian g-grandmother who, as our family knew, was born in Budafa. There is a town in our "home county" of Vas called Budafa, which seemed to be a self-evident solution. However, when a close family member with the same g-grandmother once drove through this Budafa in Vas county, "the town did not speak to her." We later established that there was a Budafa puszta in the parish of Felsöszemenye near Letenye in southern Zala county which proved without any doubt to be our ancestral Budafa.