My family is from Biala Podlaska, Poland. My father is Samuel IR, in polish it is written as JR , My aunt used JUR, she is long gone. My cousins in Israel use JUR (yud, vov, reish). As you can see, I and my siblings use IR. An interesting family.
Alexander Beider lists IR as a surname from the city of Shavli (Šiauliai), Lithuania. I don't have more information than that. But since you asked, I am wondering what is your relationship to the JUR family, would you like to connect privately?