Do trailers only used for storage need to be on O Licence?

Individual trailers are not specified on an O licence. What is specified is the maximum number of trailers which may be OPERATED under an O licence.
You may own as many trailers as you wish, and keep them at your operating centre, as long as there is sufficient additional parking for the total number of trailers which are permitted to be OPERATED.
As you have trailers which are not being operated, but are at your operating centre, it would be goid practice to display VOR boards on those trailers, and it will not be necessary to keep maintenance records for them. Any which you intend to return to service at a later date will require to be in test, and to have a PMI, before going back on the road.