Edit: Not a duplicate, the other question asking how the naming is done, my question is asking how the nakshatras were selected for naming months, the filtering rationale of left out nakshatras and how to decide the month. These are not the same questions.
Moon takes approx 27 days to orbit Earth once, so the Sky was divided into 27 Nakshatras or Lunar Mansions, and were named.
There are approximately 12 Full Moons in 1 year, so the year was divided into 12 Months. But when naming them, they used the Nakshatra names.
But there are 27 nakshatras and only 12 months, so out of 27, 15 nakshatras were taken, 9 single nakshatras and 6 nakshatras in Purva-Uttara pairs. 12 Nakshatras were left out.
And the names of the month were based on the nakshatras which are in bold in the following list.
The idea may have been, near whichever Nakshatra the full Moon occurs, that name will be the month's name.
My question is on what basis were these Nakshatras selected out for naming? There is some opinion that which ever Nakshatra the full moon would likely occur, that name is given. But full moon occurs also in the left out Nakshatras, with equal probability. So that theory is wrong.
One would expect atleast the list to be alternative or of having some pattern. But it is not alternatives and there seems to be no pattern. So how was the naming done?
Moreover how do you decide which month it is based on the position of Full Moon? Are there details about this given in Vedas, Upanishads, Ramayana or Mahabharata or Jyothisha books like Vedanga Jyothisha?