"Variant of Damir"
The name Damira is commonly a female name from the "Slavic" origin.
Damira is the feminine form of Damir, a masculine name recorded in South Slavic languages such as Croatian and Serbian and also used in Turkic-speaking parts of Central Asia. It is formed by adding the feminine ending -a to Damir. The etymology of Damir itself is disputed, with Slavic and Turkic derivations both proposed, so no single meaning can be assigned to Damira.
Damir means "To Give Peace".
The pronunciation of Damira is duh-MEER-uh.