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Wiktionary
self-storage

n. storage of one's goods in a rented commercial facility.

Usage examples of "self-storage".

Basically, I bid on the contents of self-storage lockers when the monthly payment's in arrears.

There on a stack of papers lay the answer to my prayers: a sheaf of documents, among them the receipt for Rich's payment to the San Felipe Self-Storage Company, dated Saturday, May 17.