The Asian name, meaning “smile”, was selected by members of the public in an internet vote, the zoo announced on Tuesday.
The female elephant was born on June 17th in the new Kaeng Krachan elephant compound, which was inaugurated ten days earlier.
Contestants were asked to pick between three names for the elephant beginning with the letter O, chosen for the naming of animals born at the zoo this year.
The other names were Osadhhi (a notion from traditional Hindu medicien relating to the postive properties of herbs and plants) and Ojas (force).
Omysha was the overwhelming favourite among the more than 6,000 people who voted, collecting 4,562 votes, the zoo said.
Omysha was the third offspring of Indi, a 28-year-old elephant born in Burma who ended up in the Swiss Knie Circus before being moved to the Zurich zoo in 1999.
The father of the elephant is Maxi, a 44-year-old bull originally from Thailand.
The Asian elephants are representatives of a species with a population in the wild estimated between 40,000 and 50,000, the Zurich Zoo said.
The new 57-million-franc ($63.5-million) elephant compound is named after a national park in Thailand where the zoo said it is helping to support an elephant population of around 200 animals.