So I was trying to find out what Mirzya meant (at that time I was thinking it would be spelled as Mirziya, kinda rhyming with Ishqiya, but the ‘i’ isn’t there, and it becomes a little more clear that what he said was right). He told me that Mirzya was nothing but, say, an accented version, just another way, of saying Mirza, like we say, ‘Oye Mirzya/ Mirzye’, and that was about it. I thought about how people say the name in Punjabi, and realized he was right, and the movie should actually use the Punjabi version of the name, as the story happens somewhere in Faisalabad area where the native language was Punjabi.
As for the meaning of Mirza, it’s a name that is based on a historical title of Persian origin, denoting the rank of a high nobleman or Prince, and here it’s the name of the guy in the tragic love story of Mirza and Sahibaan.
PS: If you use any Google transliteration tools, it may be difficult to write मिर्ज़्या in Devanagari by converting English letters to Hindi, as Google doesn't even show the option with half र and half ज़, the way Rakeysh Omprakash Mehra has spelled it here. Also, not entirely sure about whether the 'yay' should be there after 'meem' here or not. Correction/confirmation would be welcome.