In U.S. tax law, tangible personal property of a business that is not inventory, gives rise to a deduction for depreciation over a certain number of years, or can be "expensed" in the year acquired which is what applies to most small, not very capital intensive businesses.
To depreciate or expense an item of tangible personal property, it must be owned by the corporation, limited liability company (with more than one member), limited partnership or limited liability partners (to name some common examples).
If the business is a sole proprietorship or single member LLC, the entity is disregarded for tax purposes, so title to the property is immaterial.
It would be better practice for general partnership property to be titled in the name of the partnership, but that is not a firm requirement.
If business property is instead owned personally by the business owner or manager, there used to be two options - an itemized deduction for unreimbursed business expenses or treating the tangible personal property as rented by the company in which it is used. The itemized deduction option, however, was largely eliminated in tax legsilation passed in December of 2017 effective January 1, 302