how did it get the name?
The English-language name "Koine" derives from the Koine Greek term , "the common dialect".
Koine Greek
The English-language name "Koine" derives from the Koine Greek term , "the common dialect". 
the most common language in the eastern mediterranean during the height of the roman empire was Koine Greek.
wiki:11452710
Koine Greek [SEP] Name
The English-language name "Koine" derives from the Koine Greek term , "the common dialect". The Greek word () itself means "common". The word is pronounced , or in US English and in UK English. The pronunciation of the word "koine" itself gradually changed from (close to the Classical Attic pronunciation ) to (close to the Modern Greek ). In Greek, the language has been referred to as , "Hellenistic Koiné", in the sense of "Hellenistic supraregional language"). Ancient scholars used the term "koine" in several different senses. Scholars such as Apollonius Dyscolus (second century AD) and Aelius Herodianus (second century AD) maintained the term "Koine" to refer to the Proto-Greek language, while others used it to refer to any vernacular form of Greek speech which differed somewhat from the literary language.