The Ukrainian Г is pronounced like Gha So it's not supposed to sound like the English G I personally think that this name is beautiful only if it's pronounced correctly.
The Ukrainian г is actually pronounced like an h, just more breathy than the one in English. Still very much not a g sound though. This name is transcripted like this from the Russian language, Ganna is used by some Russian speaking Ukrainians and Ukrainians in Russia.
Ganna Walska (1887-1984) was a Polish opera singer. She was married six times, including to American businessman Harold Fowler McCormick, who promoted her lackluster opera career. She served as the basis for the character of Susan Alexander in Citizen Kane. Ganna Walska was her stage name - her real name was Hanna Puacz.