His full name was Vladimir Ilyich Ulyanov. "Ilyich" is a patronym, i.e. it is denoting his father's name, "Ilya". Accordingly, his father's name was Ilya Nikolayevich Ulyanov, "Nikolai's son". That's how russian names work.

Russian revolutionaries were persecuted by the tsarist secret police and had to work in the underground. This made it necessary to adopt a "nom de guerre", a "war name" under which he published his papers, books and pamphlets. Other revolutionaries did the same: Leo Trotzki's real name was Lew Davidovitch Bronstein, Stalin's was Josip Vissarionovitch Dshugashvili.