I'm an Argentinian with an Ukranian last name, originally written Явтушенко. My Russian father and grandmother are dead (and they didn't have a clue of its meaning, they weren't Ukranian speakers). I know that the ending шенко is very common in Ukraine, but that, in addition to a song called "Where do you go, Явтуше?" (partially translated) is all I know. Thanks a lot for anything you can tell me.
Явтушенко is a family name based on personal name Явтух and suffix -енко ("son of"), so Явтушенко is "son of Явтух". There is also other family name that is more familiar to Russian ear and has the same origins - Евтушенко.
Явтух is a short form of a name Евстихий which has Greek origins and is translated to Russian as "счастливый, преуспевающий".
Seems like the form Евтихий is more popular name of the same origin. Here is an article on Wikipedia:
Евти́хий (греч. Εὐτυχής, Εὐτύχιος, букв. «счастливый», «великодушный», «весёлый») — мужское имя греческого происхождения.
These names were given to children based on calendar of Ortodox Saints (святцы), so on the wikipedia page you can see a number of Ortodox Saints that had this name.