Pyotr Stolypin was prime minister of Russia between 1906 and 1911. He was unpopular, although clever, as I learnt when I was reading the excellent A People's Tragedy by Orlando Figes, an 800+ word page tome (error corrected - thanks to John for pointing it out) about the Russian Revolution. Figes mentioned that Stolypin's name was used to describe a couple of nasty things - the Stolypin necktie (a hangman's noose - he ordered the execution of thousands), and the Stolypin car or carriage, the train that transported prisoners to Siberia.
Stolypin is in the OED with these meanings. As one of the citations, a translation from Solzhenitsyn's Gulag Archipelago, makes clear, the word Stolypin to describe a gulag-bound train was still in use many decades after the Revolution.
What have former British prime ministers given their name to, I wonder? Well, there's Earl Grey tea, but as regards the 20th century, the answer is 'not much'. Some words in the OED are based on a particular PM's time in office eg Churchillian, Blairite, Thatcher's child, but several PMs didn't even give rise to words of that type eg Bonar Law, Campbell-Bannerman, Macmillan. Mrs Thatcher does have a presence in the Dictionary, it must be said - see this old post.
It's not unusual to give a euphemistic nickname to an instrument of torture or execution. See this post about the Duke of Exeter's daughter.