Ba'ku animals
Animals in the late 24th century on the planet Ba'ku located in the Briar Patch. ()

Named 
Rhyl

Unnamed

Fish 

The Ba'ku fish was a type of fish found in lakes on the Ba'ku planet.

In 2375, after detecting some curious readings, Lieutenant Commander Data stepped into a Ba'ku lake in an effort to ascertain the source. As he was scanning, a fish swam past him and he used his tricorder to scan it. After stroking the fish, he moved on. ()

Goat 

The Ba'ku goat was a type of animal used for farming and general labor by the Ba'ku people, on their planet. ()

Hummingbird 

The Ba'ku hummingbird was a type of bird native to the Ba'ku planet. The bird bore a strong resemblance to Earth's hummingbird.

Captain Picard and Anij watched a hummingbird fly in slow motion while experiencing the "perfect moment" in 2375. ()

Llama 

The Ba'ku llama was a type of animal used for farming and general labor by the Ba'ku people, on their planet. 

During the Ba'ku's evacuation of their village, they employed their llamas for assisting with the transport of supplies. ()

Appendices

Unused animals 

A butterfly-like creature, a pterodactyl-like animal, and a six-legged turtle-like animal were among dozens of animal designs, possibly native to the Ba'ku planet, included in a children's picture book produced for  by scenic art supervisor Mike Okuda. (The Secrets of Star Trek: Insurrection, p. 64) 

However, only the front cover of the book ended up visible in the film. The prop book was sold off on the It's A Wrap! sale and auction on eBay in 2007. 

None of the Ba'ku animals (including the rhyl) were referred to by name in the film. Their monikers either derived from behind-the-scenes sources or from their closest Earth counterparts.

de:Liste der Tiere von Ba'ku
 
 
Unnamed² species