Mugi, as I posted on page 7, I honestly think that the Forest's name deletion is broken. That is, it deletes the pet from the database, but not the name. So the name still acts as taken although the pet doesn't exist anymore.
To check the theory, I tried the following: found a pet in the forest, but before clicking yes or no, I looked up the name in a different window. It says there is 1 pet with the name. Then I clicked not to adopt, so the pet should be completely deleted, and the name free. Instead the name search still says that there is 1 pet with that name. And when I tried to look up the pet according to species in the search, it does not show up any more in the alphabetical list. You can try the same if you want to, if you find a pet in the forest and choose not to adopt it (best ones are those with the letter A or only numbers, so it won't last ages to look them up in the search).
Also I have looked up all Zenirixes in alphabetical order, and Hanrin is not among them at letter H (I can take screenshots if necessary). So I am 99% sure that happened to him. It would be best to ask someone from staff to look into this matter. I am sure they have a more effective way to look up pets by the name. And if the pet really is deleted, they could delete the name too, so the system would allow you to rehatch him.