Yes, in Ukrainian it's Heorhij. The Russian language, indeed, does not have the "h" sound, but the Ukrainian language does.
Russians very often transliterate "h" as either "g" or "kh" ("x"), creating a lot of confusion. For example, they say and write, "Okla*kh*oma." Ukrainian immigrants, mocking those Russians who say and write "Oklakhoma," even composed a funny poem about it. In Ukrainian, it goes like this:
"Zvuku "kh" u movi anhlijs'kij nema,
Tozh khaij bude vsim tse vidomo,
Shcho prozhyve bez Oklahomy Khoma,
I bez Khomy Oklahoma."
("There is no "kh" sound in English, so let the whole world know that Oklahoma will survive without Khoma ("Thomas" in Ukrainian, indeed with the "kh" sound), and Khoma will survive without Oklahoma.")
Russians also say and write "Gitler" (meaning Hitler), "Khaidegger" (meining Heidegger), etc.