And as long any of these plants was not making it solely for their own behalf, the customer could label it either with the proper namer or any other name depending on his will to pay licences for a trademark.
The trademark Rodinal was licensed to a company who purchased a business from Agfa in a package deal.
This company decided not to bottle and sell B&W chemistry as the volumes were not interesting to them.
At that time the chemistry in bulk was still available from Vaihingen but later this changed.
The AgfaPhoto trademark licensing contracts do not allow sub licensing and the current license holder did not consider manuacturing of Rodinal a business.
This was when the name dissappeared from the bottle regardeless if one was theoretically willing to pay for it or not.
One could say "the name got stuck" in this legal setup.

I guess by "After the stop of production in Vaihingen" you mean the end of production as Agfa plant. Or do you refer to an end of production of Rodinal at that plant?
The plant in Vaihingen does not manufacture Rodinal anymore. First finishing was stoped and later on the entire b&w production. This plant has been built to effectively produce large amounts of chemistry. They are not set up to manufacture small amounts of niche market products and manufacture other, non photographic, products now.

The last we could purchase were the leftover bottles and caps. We ran out of Rodinal shaped bottles but still have thousands of NEUTOL 1,25 L bottles.

We employed former Agfa technicians, made laboratory scale productions, verified the recipes and handed them to a new manufacturer for mixing on a lage scale. We then bottle, cap and label ADONAL in our factory.
This allows us to keep stock fresh. In the original large bucket Rodinal stays clear forever. Once bottled in the thinner-wall PE-bottles it starts to darken.
Our competitors took a bottle of Rodinal and handed it to a new manufacturer asking him to clone it, which he did. Foma sells what we have ben selling under the APH09 name. This is Rodinal is made acording to the recipes from Wolfen (ORWO) and yet made in a different factory but not by Foma.

The largest difference is between this old Rodinal sold by Foma as R09 and by us as APH 09 and the two others. The reformulated "clone" is similar to ours yet not identical. The pH values have been brought in line between R09 and Rodinal acording to our request in 2002. Since then all developers have more or less the same development times.