Why were these groups called monasteries and how did they choose their members

The name probably originates from the name for the members, monks, who were male members of strict religious orders. Generally, one became a monk though one's family making arrangements, and often fathers would volunteer their children from a young age. Young women were also registered as nuns in abbeys, the equivalent of a monastery for a woman. 

Very useful. it is to learn because history repeats itself so learning about it those mistakes not happen again.