Sean Monahan wore #20 for the Ottawa 67's when the Flames drafted him. He never went back, instead making the NHL right out of his very first training camp in 2013, when the number belonged to Curtis Glencross.
Monahan was basically guaranteed to have a longer, and better, career than Glencross, but it had been his number for quite some time. It would have been bad form to change it - and so, Monahan got #23, which the Flames gave him off the bat.
It's stuck. And it's kind of fitting, what with linemate Johnny Gaudreau wearing #13 and all.