That was the way things were done in the past, so the Ukranian "Hohol'" became the Russian "Gogol'". It's different now. Russians trying to sell souvenirs to tourists are always yelling "Army Khat! Army Khat!"
I’ve heard both. In yeshiva our lunch lady would say when she was out of something everyone wanted: “I kno khav. Eef I khav, I geev, but I no khav so I no geev.” But if someone was taken to the ER at the hospital, a Russian would say “khee taken to gospital.” The French just elide their H-es, as do Cockneys in England, except they also stick an H at the start of a word that begins with a vowel. So “ ‘arry’s tayken hill, so ‘e ‘as.”