How would you say "X, the Y" in Chinese?
Domestic animals like dog, cat, horse, cow, pig, goat, chicken and duck are often described with a single syllable word in Chinese:

狗，猫，马，牛，猪，羊，鸡，鸭

There are few exceptions, For example, snake is not a domestic animal, but it is still being called with the single syllable word 蛇

For other animals, it is customary to use two syllables words to refer them. 

For example: 

Tiger (虎), is always called 老虎

Elephant (象) is always called 大象

Monkey (猴) is always called 猴子

Frog (蛙) is always called 青蛙

In the case of moth(蛾), it is always called 飛蛾

So, your should refer your pet moth as  '飛蛾'

Calling someone by a single syllable name is rare because it sounded blunt. Most of the time we would add title or a name prefix (indicates a noun is a name) to make it a two syllable name.

For example: 

The name '七' would be '小七, 阿七 or 七仔' in day-to-day conversation

In your case, "my pet-- Seven the moth" should be translated as '我的宠物--  飛蛾小七 (or '阿七)' 

Or you can say: " 小七, 我养的飛蛾" (little Seven, the pet moth I keep)

Edit: one more suggestion: 

Since you called Chinese character as kanji, here is another suggestion-- 'Seven' in Japanese is なな (nana). You could call it '娜娜(Nana), which is a common female pet name.