Olha is Ukrainian version of Olga, which is female name popular in
Eastern Europe and Latin America. Name originates from Scandinavian "Helga". To Kievan Russ (Ukraine now) was brought with invited Scandinavian Princes around 500-600 AD. But became popular around
introduction of
Christianity around 900 AD. Well-known is Princess Olga, grandmother of Prince Volodymyr the Great (the one who made
Christianity Official State Religion). She was the first Christian Princess in Kievan Russ, big fan of books and education. I believe, she was the single cause of popularity of the name in Slavic countries. Not many people new she wasn't from noble family, but a daughter of ferryman. She driving paddle ferry across the Dnipro River and that is there Prince Igor spotted her. She had many sons. After her husband was killed during tax ride, she sorely ruled country until her oldest son reached adolescence and was closely supervising state offers until very old age.
Stereotypically, attributes of this great princess are applied to all Olgas. Name is
particularly popular among Ukrainian Diaspora. There is no difference in how Ukrainians or Russians pronounce the name in their native language, but there is difference is how they spell their names in English. You can see the origin by differed spelling - Olha (Ukraine), Olga (Russian speaking countries, Poland, Latin America).
For short - Olia, Olichka, Olyunia, Olka, Olana.
There are also male name Olga in use in Turkey