No, you really don’t, because it really isn’t. It is the socialized ownership.

Modern society involves states. If you want to try and tell me that socialism is whatever you think it is, and everyone else is totally wrong and socialism isn’t about state ownership, be my guest. I don’t really care and I’ll just consider you to be another statistic in the list of people getting it wrong. There is no requirement for it being just workers owning it. We, modern humanity, form state based societies. If a society socializes the MOP, it is run by the state.

This is why Marx saw socialism as the in between step. The state would take ownership of the means of production, socializing the gains/costs, before eventually the state dissolved into worker owned communal situation in a stateless society. If there is no state then there is no socialism in the common interpretation. There are other terms to specifically define what you are referring to.