When you build it yourself you get to name it. When it’s city (public) money you don’t.

Sonsorship subscriptions are fine though. I’d even suggest that a certain portion must be set aside in a fund that generates interest or investment revenue.

putting a “maintenance of this made possible by sponsorship of xyz” on a plaque makes sense to me. But sponsorship should be a subscription, not a one time payment.

An important thing to add to this, I think, is that it's important that the sponsorship has no final say in the direction, or management of the asset. It should just be treated as an advertising/philanthropic opportunity for the sponsor.

One concern that I do have is over-reliance and dependence on the sponsor. It would not be great to have a situation where the City is beholden to some corporation.