We have names for days in a week and for months in a year, but does a convention exist for weeks in the month? Alternatively, do we have names for weeks in the year other than, say, "The 34th week of 2018"?
If you really wanted to have a system for this, for Catholics or the traditionally-minded religious,
are specially named weeks throughout the year. (The term “octave” is misleading to us moderns. They’re reckoned as lasting eight days by counting inclusively in the ancient Roman manner: i.e., they’re actually 7 days long.) The big ones are the octaves of Easter, Epiphany, and Christmas although there are 15 other specially-handled weeks as well.
This obviously has very little pull in the general secular system, even if it is named after a pope. Even the Church itself generally thinks in terms of Eastertide (50 days) and Christmastide (12 days) rather than the octaves in its general planning.