Where does “鹿沼” come from?

鹿沼 (Japanese) comes from Japanese 沼, from Japanese 間, from Middle Chinese 間.

Ancestry of “鹿沼”, step by step

Step	Language	Word	Meaning
1	Japanese	沼	a swamp, a bog, a marsh, a wetland
2	Japanese	間	interval; "suffixes some expressions of time to...
3	Middle Chinese	間	—