3 Answers

The roots of names ending with -ian/-yan are typically first names, such as Petrosian "issued from Petros", Simonian "issued from Simon", etc. When the name ends in -lian or -(d)jian, the root is expected to refer to a location or a profession, respectively. Thus, the etymology of Vanlian is literally "issued from the man from Van" and that of Kebabjian is "issued from the kebab merchant". However, an ancestor's occupation will not necessarily contain the suffix -(d)ji, thus Vardapetian/Vartabedian  translates as "issued from the vardapet", Bjishkian as "issued from the doctor" and Keshishian as "issued from the priest".

The -ian/-yan suffix may also, but more rarely, attach to an adjective denoting a quality. Thus, Bzdigian/Pztikian translates as "issued from the small (man)", Medzian/Metsian as "issued from the tall (man)", Ganantchian/Kanantchian as "issued from the green, i.e. young (man)".

Some former noble Armenian names, such as Artsruni/Ardzruni are still in use today. When they moved from Armenia or from the Middle East, some changed their last names to adapt better to their new societies. Sometimes the -ian or -yan ending was dropped and the root kept, such as Charles Aznavour (was Aznavourian), or Andy Serkis(originally Sarkissian). Other times the name was translated, as "Tashjian" (which is derived from Turkish word 'ta' meaning 'stone') becoming (approximately) "Stone".

From Wiki.

I got the idiot's version, quite simplified. "ian" was "son of the" and the profession preceeded it. Allegedly, there is a painter among my ancestors, most likely house, not canvas. 

I was arrested at link Occupy Los Angeles in 2012 and my grandfather died shortly link thereafter he says. "I had no money at the link time but a dear friend gave me a 'buddy pass' to fly back to LA for my arraignment. The thing about those passes is that they don't guarantee you a spot on the plane. I ended up missing every single flight that day and I arrived at LAX three hours after my arraignment."