I know of no hard and fast rule on crediting donors of collections and
exhibit items by indicating their names on the labels.

But there is a strong element of goodwill involved that weighs heavily in
favor of giving visible credit where it is due.  The credit line certainly
doesn't detract from the museum's quality.  In the case of a startup
museum, credit seems to me to be especially valuable as a way of enhancing
relationships with the support constituency.
In a small town, it is not just valuable, but almost a prerequisite.