According to the Red Book of Westmarch,
In Middle-earth, Ursa Carnimírië was a

Angry Wood-Elf

Elven Name Possibilities for Ursa Carnimírië
The root name suitable for feminine and masculine is:
Thaurdol
Another masculine version is:
Thaurdolion
More feminine versions are:
Thaurdoliel
Thaurdolien
Thaurdolwen

Hobbit lad name for Ursa Carnimírië
Doderic Fields from Deephallow
Hobbit lass name for Ursa Carnimírië
Melilot Fields from Deephallow

Dwarven Name for Ursa Carnimírië
Gimli Redarmour
This name is for both genders.

Orkish Name for Ursa Carnimírië
Thrakbog the Horrible
This name is for both genders.

Adûnaic name for Ursa Carnimírië
Aphaphurdam

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Heh, Angry Wood Elf! Funny!! And I love the hobbit lass name Melilot; it means something like "beloved flower".

 The Elf Witch of the Night