In Hebrew the full name is KHISKIYA (with a CH-sound in the beginning like in LoCH Ness) and it means: "God (or rather:
Yahweh) is strong / has proved strong". Thinking of a reasonable name giving motive you may think of God's power to bestow a child onto the mother or else to help with the birth.
I can't find ZEKIAH in any of my books, but it is obviously used as a given name. And it sounds quite convincing that it should be a short form of
HEZEKIAH. If you believe it is, it is. So be happy with it.
Andy ;—)