Neko.
In Japanese, your name would be pronounced Kotreina. They don't have the "a" sound as in "cat." Therefore, all short a sounds would be turned into a short o sound.
Neko is the japanese word for cat or "kitty".
In Japanese it means Maka Paka. In Afican Maka is Earth and Paka is cat. So it is Earth Cat.
The lucky Chinese cat is called Maneki Neko in Japanese.
"Neiko" is not a Japanese word. It does not have a specific meaning in Japanese. It could possibly be a personal name or a non-Japanese word.
Sagwa
The name Alexandria doesn't mean anything in Japanese as it's not a name of Japanese origin. However, it may be written in Japanese as アレクサンドリア (arekusandoria).
The name Gibb in Japanese would be written as ギッブ
Nekomimi is the usual term. It's non-gender specific and translates literally as 'cat ears'. Neko-kun or neko-chan would be polite terms to address a real live kitten.
Princess cat would be pronounced as neko hime ( neck-oh he-may).
neko is Japanese for cat
Red cat is aka neko in Japanese.