Many also refer to her as simply "Peaches," for obvious reasons. The Japanese nickname is "Momoko."
A popular paring for Tenshi is TenShion (Tenshi X Shion), because of Antinomy of Common Flowers' ending. (Shion became best friends with Tenshi at the end of the game, if you didn't already know.)
Fans have compared her and Flandre Scarlet to Chuuya Nakahara from Asagiri's manga series Bungo Stray Dogs.
*The reasons are because Tenshi and Chuuya's abilities revolve around earth manipulation.
The peaches on her hat are also depicted in fanworks to be her source of power.
Due to her apparent eagerness to be beaten up by the other characters in SWR's story mode (with dialogue lines such as "Yes, get angry! Because if you don't punish me, Gensokyo shall be no more!"), she has gained a reputation as a masochist. Probably that is why her masochistic feeling of ecstasy is called, instead of "zecchou", "uchouten"(有頂天), which should originally means one's bad mind, "be in excessive glory".
As a result, she often appears along with Yuuka Kazami in some fanworks.
This, in addition to her toughness, leads to Tenshi having a high defensive stat in various fangames.
For some reason, various fanworks show Yukari Yakumo to hate Tenshi, or at the very least, they're at odds with each other.
Tenshi is often depicted to have a flat chest. This is likely because of her childish behavior, but it can also be taken as the result of her toughness. As if she's as tough and flat as a wall.