...until just a few moments ago I never realized that there are (that) many Kellises around the world, and in particular outside Greece!
I read that the name may have Scottish origins. Maybe so, but from what I know surnames ending in ("is") are very common in Greece, and you get a lot similar to Kellis (Mallis, Vellis, Mellis, Tellis etc.). The Greek version is written ("ÊÝëëçò") - you might need the fonts - , while the double 'l' occurs due to the language.
Origins dating back to the 19th century are not very clear to my family. My grandfather (same name) was born in the what is now part of Turkey sea land facing the aegean sea (Greek sea), in 1915 in Smirni (now called Izmir in Turkey, population 5 million), and passed away last year.
I've heard various stories about our name, including some versions of what it means (good horse rider, bold(!) being some of them), and also rumors that is may originate at the island of Crete (south Greece). I met 4-5 families around Greece, all seem to have came from the same area..
I grew up in Thessaloniki, second biggest city in Greece, along with a couple of more Kellis families (one with close relatives/cousins, one with far ones). I currently live in the UK.