In Russian, Г is [g] and [h] doesn't exist. Hence a Russian would pronounce his name "Gonchar".
In Ukrainian, however, which also uses the Cyrillic alphabet, but a slightly different version to it (same as how German has a modified Latin alphabet, because it's added the letters ä, ö, ü and ß), Г is [h], and they have a separate letter, Ґ, for [g]. So a Ukrainian would pronounce his name "Honchar". Because Russian does not have these two different letters, they've merged both sounds into the one letter.
Similarly, the letter i doesn't exist in Russian, but does in Ukrainian, so they've Russified his first name too.
Serhiy Honchar is Ukrainian, so it is perhaps best advised to use the Ukrainian version. Unless you want to say that FDJ's sprinter is "Evgeniy Gutarovich", which is the Russified version of his name.