How about - Always There Storage or Always Available Storage? Gets you up top in the yellow page listings........give a description of your company some how.

When I owned my own chocolate store, we picked three names, went out to local restaurants that we frequented and gave them the names. Came back two to three weeks later and asked them which one they remembered! Everyone came back with the same name. "My Sweet Shoppe", "The Sweet Shoppe", and "Friesner's Fudge". All remembered the first one - which was not mentioned in the same order when we gave out the names........just a suggestion........