There are multiple origins and meanings for the name:
1. Armenian (Տիգրան) name, comes from the ancient Greek word (τίγρις) [tigris] "tiger"
2. Parthian name [Tigrarāna] derived from the words tigra “arrow” + rāna “fighting”="archer, bowman".
The name of the ancient Armenian king.
Tigranes the Great (or Dikran) (b. c. 140--d. c. 55 BC), king of Armenia from 95 to 55 BC, under whom the country became for a short time the strongest state in the Roman East.