What is that, four different pronunciations of Kateri - and none of them particularly similar to mine? I nearly had her as my confirmation saint (I am fully aware she isn't actually a saint), and was thinking it was more like "kuh-terry", with an emphasis on the 'ter'.
My daughter is named this and we pronounce it ka-TEER-ee. When we went to the shrine of Bl. Kateri in Auriesville NY that is how people were saying it, so that is what we stuck with.
Kateri Tekakwitha is no longer Blessed -- she was recently canonized: St. Kateri Tekakwitha. I know several people with this name, and they all pronounce it differently: -- kah-TEER-ee (I've been to the Shrine of the North American Martyrs in Auriesville, NY many times, which commemorates St. Kateri [among others], and it does seem that kah-TEER-ee is their preferred pronunciation) -- KAH-ter-ee -- kah-TEHR-ee -- GOD-ah-lee (The parents of the girl with the GOD-ah-lee pronunciation [spelled Kateri] met a Native American woman with this name, who told them that GOD-ah-lee is the authentic Native American pronunciation)
The girls and women I know with this name range in age from newborn to middle-aged.