So... is Damekko Doubutsu finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: February 21, 2005
Manga finished: April 27, 2020
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Damekko Doubutsu follows Uruno, a decidedly un-wolf-like wolf, as he seeks a new home. He stumbles upon a forest populated by animals that are far from typical examples of their kind.
Initially, Uruno is hesitant to stay, especially after an encounter with the ill-tempered Usahara. However, his resolve crumbles when he meets the endearingly clumsy Chiiko.
Smitten with Chiiko, Uruno decides to remain in the forest, hoping to win her affections despite his own perceived inadequacies.
The anime explores Uruno's life in this unusual community, surrounded by its cast of eccentric and "useless" animal residents.