"Toramaru" can be literally translated as "tiger circle". However, the word "maru" is also used to end the names of ships in Japan, which is fitting, considering one of the main aspects of Undefined Fantastic Object is the "treasure ship".
"Shou" means "star", which is also fitting considering the extraterrestrial implications given by the game's title.
Shou's ability is listed as "The power to attract treasures". Ironically enough, however, she herself did not gather any of the needed treasure to unseal Byakuren; instead, Nazrin found the pagoda, and the heroine found the fragments of Tobikura. The only real reference to this ability is in her final spell card in Double Spoiler.
Shou's BGM description lists her name as 虎丸星 instead of 寅丸星. 虎 "tora" can refer to tigers, felines of the "panthera tigris" species, or colloquially, a "drunk person". 寅 "tora" can be used to refer the tiger as a sign in the Chinese Zodiac, which carries with it the additional meanings of a period of time from 3AM to 5AM, the direction East by Northeast, or January.
Her appearance seems to be based upon that of Bishamonten, the Japanese equivalent of Vaisravana, who is often depicted holding a spear and a small pagoda. This is derived from the fact that Chougosonshi Temple (朝護孫子寺), which keeps the e-maki of Myouren's tales (Shigisan Engi Emaki), enshrines Bishamonten. Originally, the tiger was only somewhat related to Bishamonten, but became even more relevant when the Buddhist groups in Asuka period, Shoutoku taishi and Soga shi, subdued the anti-Buddhist group Mononobe shi because Bishamonten appeared in front to support them at the hour of the tiger on the day of the tiger in the year of the tiger (寅の年、寅の日、寅の刻) of the Chinese zodiac. Now, many tigers can be seen at Chougosonshi Temple. Their website also shows how they raise them.
She may have been inspired by one of Vaisravana's frequent companions in artistic depictions and sutras, an unidentified man wearing a tiger skin. She may also have been inspired by his usual mount, a Snowlion, but as Snowlions are more similar to dogs than to tigers, this seems unlikely.