Does a Minecraft server (city build) without a website also need an imprint?

I recently got a small Minecraft Citybuild server that doesn't have its own website yet. Does this then also need an imprint or only as soon as we have a website?

We somehow earn money? Or do you offer this as a service?

No, no transactions, all freeplay, soon there will be a shop with an imprint. Do we brew one beforehand?

No, if you think about it, you would realize for yourself that this is technically not possible.