Please do not simply vote No because of Fan Myopia. Try and think whether or not the trope is broken instead of whether or not people should know who the trope namer is.
Pros: The name is unintuitive if you aren't familiar with the Harry Potter stories, and the patterns in the wicks seem to suggest that people are mainly remembering that there's a trope named after Umbridge and not what it means.
Plus possible renames still include Umbridge remaining the trope namer, just more context than "The".
Umbridge also only appeared in two books, the 5th and the 7th. Unlike other standing HP Trope Namers like Ron and Draco, Umbridge is less likely to have lots of Popcultural Osmosis.
On a check of around half the wicks, potholing on Umbridge's name takes up more than half, but unambiguous misuse takes up less than 10%.
The main arguments for and against potholes to Umbridge's name being had are here and here respectively. It should be noted, however, that The Umbridge is not a characterisation trope, but a device trope.
Cons: The Harry Potter franchise is so popular that a sufficiently large number of tropers are expected to be familiar with the character, most of the potholes to Umbridge would not be bad if they were any other character, and the rate of unambiguous misuse is very low.