Wow it's a fascinating question. I have never thought about that before and this question intrigues me. Because it's a two characters word, meaning that it definitely has an origin, not like the word 猪 for example, which just reassembles the image of a pig.
After searching a while and came across many different sources and non-senses, you might actually be right. The earliest usage, that I can find, of the word 水母 means the goddess of water. First used in 先秦, which is the period from 221BC to the possible known beginning of China.
However the first record of using this word, again that I can find, appeared in Verses of Chu 楚辞, which is a collection of poets of a greater period of time. The word came from 王襃．九懷．思忠, written as：「玄武步兮水母，與吾期兮南榮。登華蓋兮乘陽，聊逍遙兮播光。」The author 王襃 was living at the time around 6 century AD (possibly 513 - 576). The word 水母 in this poet means the same, the goddess of water.
A more recent variation of the goddess, is called 水母娘娘, or the Old Mother of Water
According to Chinese folklore, she is responsible for submerging
Sizhou/泗州 (an ancient Chinese city located in today’s
Jiangsu/江苏 Province) under the waters of lake Hongze Lake/洪泽湖 in 1574
A.D. and is currently sealed at the foot of a mountain in Xuyi/盱眙
So my best guess is when people saw this amazing creature in the sea, they would see it as an avatar of the goddess of water, and thus call it 水母.
We also call it 海蜇 nowadays, but this word feels more like "beef", while 水母 feels like "cow" or "bull". Both names are quite common to use.
Also, in 本草纲目, it's called 海䖳.
I have never seen this word being used as Medusa.
- Werner, Edward Theodore Chalmers (1922). Myths and Legends of China (PDF). Courier Corporation. pp. 166–168.