Probably a rare variant of Katina or Katherine, from Greek roots meaning "pure."
Cotenia is probably a rare variant of Katina or Katherine, names ultimately tied to the Greek root meaning pure. That connection gives the name a classical base, even though the spelling itself feels uncommon and embellished.
The longer, ornamental shape of Cotenia makes it feel more elaborate than Katherine or Katina, with a softer and more decorative rhythm. It has the air of a vintage or regional variant that has been carried forward into modern use. The name feels feminine, distinctive, and quietly graceful.