Russian names are generally given name then patronymic (i.e. 'son of' or 'daughter of') then family name. A person is formally addressed by their given and patronymic names.
In this case Felix Edmundovich would refer to Felix Edmundovich Dzerzhinsky.
I agree. This leads to the question what the heck Bing is translating here.
It's algorithm is probably associating words or ideas with equivalent but not identical best match in English - if you translate First Patronymic of some famous dude (famous enough that the bingbot has a lot of Russian and English text about them to learn from) it'll spit out the English First Last - as the patronymic will rarely be used in English articles about them. In that way First-Patronymic serves as sort of a dual-index on the Russian half of the Russian-English translation. Just a guess