I am not exactly familiar with the way Bulgarian Turks form their names, but I know that nowadays a lot of them choose to put the father's name without the Bulgarian -ov/-ev (-ova/-eva for girls) in the end. So Myumyun
Rosie Myumyun would be Myumyun, son of
Rosie, grandson/offspring of Myumyun.
And yes, the li'l guy's name is Myumyun Myumyun. In Bulgaria it's quite common to name a boy after his paternal grandfather who in most cases gives the last name. The US equivalent would be
John Johnson, the South American -
Rodrigo Rodriguez, etc. I know 3 boys by the name of
Ivan Ivanov, and those are not a rare occurrence, believe me =o). Also, I am not sure all the other Slavic people have that "dispay of variety", so it must be the Slavic way plus Eastern European traditions.
I hope that clarifies some things (or at least, doesn't confuse anybody :P)