Water purslane appeared today because I was wondering why Herr Ludwig might not want this genus named for him. Who wouldn't want to be memorialised through the ages in that way? I speculated that this unassuming but common plant could be the reason. It is designed to attract little attention. Apparently that worked. Rather than first describing and publishing this local species, and realising it was a relative of those showy plants, Linnaeus published the name Ludwigia in 1753, and described L. perennis, a species of India. Water purslane was published at the same time, but was called Isnardia. Now I can wonder who Isnard was?
The first species on which a published description is based are called the type species. Type specimens are carefully preserved. Botanists can then refer to them if there are future questions about the classification. That is, of course, frequently happening these days, as their genome is explored. If the genus name is changed, are they still type specimens? Yes, unless the genus is abandoned altogether. At the University of Michigan herbarium, the type specimens are safeguarded in a special section. I imagine that's a typical process around the world.