It depends on the context, but in production logistics the term "space utilization rate" is used by SAP (the market and technology leader in business management software).

Definition of "Space Utilization Rate": A percentage of warehouse space utilized (i.e. filled) versus maximum available warehouse space. The utilized and maximum spaces could be pallet positions, bins, square feet, cubic feet, or any other space metric provided that the units remain consistent for the two measures.
http://www.benchmarking.sap.com/confirmation/Help/WMS.html

I have also seen the terms "storage utilization (rate)" and "storage space utilization (rate)". The word "rate" can be replaced by the word "percentage".

All these terms should really be preceded by the word "warehouse" to narrow the context, since for example the term "space utilization" can be used for IT file systems, servers, in fact anything with available capacity that can be filled to a certain degree.

Another term "fill rate" is often used in Sweden as a translation of "fyllnadsgrad" but there seems to be some confusion as to its actual meaning. "Fill rate" is normally defined as "percentage of customer or consumption orders satisfied from stock at hand", ie order fulfillment.

Unfortunately, "capacity" is a mistranslation in a logistics context since it refers to total space and not percentage of storage space utilized.