Please read the Background and the Guiding Philosophy. There is enough proof and co-relation of facts, if one does a statistical regression. Also document all known syllables, and take the probabilities of the sounds happening together in different combinations, and you will get the answer. The fact that like-wise words are found in different places, indicates human-interaction between the places.
Casimir is a last name as in "Hendrik Casimir" or Casimere in "Corey Casimere"
Kashmir is the name of state in India, and many people have names go by Kashmiri, Kasi-Meer.
"K" and "C" get mixed up in the English transliteration and has overloaded sounds, "Cat" and "Champ".
"S" and "Sh" get mixed up becuse of aspiration tendency of Europeans and Americans.
"E" and "I" are the same, as "E" is overloaded as "Hey", "Sell", "Meet", where you can see "e" is "ai", "e" is like "a" and "ee" is like "ii" respectively of Sanskrit.
Meer, Mir, and Miir, are same, which in Sanskrit means, "Ocean, Limit, Boundary, Mountain".
Now feminine name will be formed by adding "a", which beccomes, "Meera" or "Miira", "Mira", assuming "r" as a built sound of "a".
Now Kashi was a well known place of learning from the ancient times, and Kashmir was a swampy mountaineous place reclaimed by Rishi Kashyap (there is more than that which I need to dig), and it also became a seat of learning for people from the West Asia.
So a place which becomes the source, or the limit, or the ocean, or the mountain of the Knowledge, or the Fountain Head of the knowlege is called "Kashimir"!
Now later the word "Meer" became an addressing of honour, like the word "Sir", perhaps designating a person's stature as an educated person and knowledge. In the ancient times there was more respect given to knowledge and learning than the material belongings one had.