Greetings from Solveig!
>> I was under the impression that "Tenshi" is a title for the
>> Emperor or
>> Empress, as it translates to "Son of Heaven." Anybody have any more
It's all in the kanji. The version that might look like a name 天子
(heaven child) does indeed refer to the emperor or someone else that
rules the kingdom (see Daijirin). Christian missionaries came up with
neologisms to describe various things not necessarily already present
in Japanese culture. Their word for angel is 天使 (used by heaven/
heavenly messenger) and sounds the same (see Daijirin). However, this
tenshi does not look like a name.
Actual christian baptismal names were transliterations of Iberian
names like Elizabetta (see Nihon no Joseimei). While Angel may sound
feminine in English, I believe that it is most likely a masculine
name in Iberian cultures. This of course does not answer whether or
not it was actually used as a baptismal name in sixteenth century
Japan or how it would be transliterated into the Japanese sound system.
Your Humble Servant