I’m quite sure Barsoomian is Armenian. If Iranians have ‘ian’ names I would suggest it is because Armenia share a border with Iran and there have probably been a good deal of migration over the centuries.
Barsoomian is almost definitely Armenian. Some Iranians have “ian” names, but it is not necessarily because they have an Armenian minority and neighbor Armenia. Rather, it is because many Iranian last names were created in the early 20th century, and came from names of places or occupations or things like that, just as European names do. That could lead to using “ian” in the way that in Spanish is “ero” or in English is “er” as in shopkeeper, cooper, tanner, shoemaker.