Of course you can name your character how ever you want, but if you have problems finding a name for your character, then you can look here.
Here is a list of good name generators that might help you choose the perfect name for your character.

If the generator offers first name and last name, you can choose one of them or both.

Arctis
In Arctis birds have mostly nordic or Inuit names
Danish name generator
Finnish name generator
Norwegian name generator
Swedish name generator
Inuit name generator

Villa Corvida
In Villa Corvida, birds have mostly european like names with a medieval sound to them
Old German name generator
Renaissance English name generator
Renaissance Italian name generator
Renaissance Spanish name generator
Renaissance German name generator
Renaissance French name generator
I know these aren't very medieval-esque, but it was the closest I could get

Ancient Oaks
Animals that live in this place have often names that might sound like names for elves from fantasy books and movies
Elf name generator
Half-Elf name generator
Dragon Age Elf name generator

Eastern Plains
Habitants of this area have most often Slavic sounding names, like Russian, Croatian or Czech
Slavic name generator
Ukrainian name generator
Croatian name generator
Czech name generator
Serbian name generator
Russian name generator
Polish name generator
Slovak name generator
Slovenian name generator

Lakes
Here the most common names are French sounding ones
French names generator

Irbis Mountains
In the mountains most common names are German in lower levels and Tibetan sounding names in the highest areas
German names generator
Tibetan names generator

Endless Caves
Here most common names are antique Greek/Roman ones
Ancient Greek name generator
Roman name generator

The City
Birds here can have pretty much any kind of name, but mostly they have common English names or names for pet birds
English name generator
Pet bird name generator
Bird of Prey name generator

Ugwadule Desert & Lion's Realm
In the desert birds have mostly African sounding names
Swahili name generator
Ndebele name generator
Zulu name generator
Arabic name generator
Egyptian (Ancient) name generator
Egyptian (Modern) name generator
Somali name generator

The Jungle
Names for habitants of the Jungle are usually tribal sounding, Brazilian or Mayan/Inca
Brazilian name generator
Mayan name generator
Tribal name generator

Red Mountains
Most common names are Native American sounding ones
Native American name generator

The Ocean
Animals here can have pretty much any name that comes from areas near ocean

Dragon's Blood islands
On these isolated islands the most common names are Aboriginal names
Aboriginal name generator

Ice Plains
Practically every "normal" name is possible here. Seen the movie Happy Feet? You can take your inspiration here

The Aztecs
Could it be different? The names here are mostly Aztec ones, from the language Nahuatl
Aztec name generator


Other useful name generators:

For birds
Kenku name generator
Aarakocra name generator
Tengu name generator
Narnia Owl name generator
Owl name generator

For bats
WoW Bat and Dragonhawk name generator
Bat name generator

For jaguars (mostly loners)
Tabaxi name generator
Cathar name generator
Khajiit name generator

Any
Chinese name generator
Korean name generator
Thai name generator
Japanese name generator
Japanese (Edo) name generator


Suggest generators below↓