The Velvet Underground was a book about the sexual underground of the early '60s by Michael Leigh that Cale's friend Tony Conrad showed to the group. Reed and Morrison have reported the group liked the name, considering it evocative of "underground cinema", and fitting, due to Reed’s already having written "Venus in Furs", inspired by Leopold von Sacher-Masoch's book of the same name, dealing with masochism. The band immediately and unanimously adopted the book's title for its new name.

The Exploding Plastic inevitable was a show created by Andy Warhol to introduce The Velvet Underground & Nico. The group opened in New York and toured the United States and Canada. This was the way some critics responded: "Suddenly the intermedia shows are all over town. The Velvet Underground performances at the Dom during the month of April provided the most violent, loudest and most dynamic exploration platform for this new art. Theirs remains the most dramatic expression of the contemporary generation. The place where its needs and desperations are most dramatically split open. At the Plastic Inevitabile it is all Here and Now and the Future." "Screeching rock'n'roll- reminded viewers of nothing so much as Berlin in the decadent 30's." "A Three-ring psychosis that assaults the senses with the sights and sounds of the total environment syndrome...Discordant music, throbbing cadences, pulsating tempo." "Not since the Titanic ran into that iceberg has there been such a collision as when Andy Warhol's Exploding Plastic Inevitable burst upon the audiences at The Trip Tuesday. For once a happening really happened, and it look Warhol to come out from the New York to show how it's done. The Velvet Underground is so far out that it makes the tremendous thumping beat of the great, groovy group which opened the program sound passé." "Warhol's brutal assemblage-non stop horror show. He has indeed put together a total environment, but it is an assemblage that actually vibrates with menace, cynicism and perversion. To experience it is to be brutalized, helpless-you're in any kind of horror you want to imagine, from police state to mad house. Eventually the reverberations in your ears stop. But what do you do with what you still hear in your brain? The flowers of evil are in full bloom with the Exploding Plastic Inevitable." "Shatteringly contemporary - the electronic music, loud enough to make the room and the mind vibratein unison - Nico, the beatiful flaxen-haired girl, the noise, the lights, the film and the dances build to a screeching crescendo." "The Velvet Underground, a group whose howling, throbbing beat is amplified and extended by electronic dial-twidding, has a sound hard to describe, even harder to duplicate, but haunting in its uniqueness. And with the Velvets come to blonde, bland, beautiful Nico, another cooler Dietrich for another cooler generation. Art has come to the discotheque and it will never be the same again." "The sound is a savage series of atonal thrusts and electronic feedback. The lyrics combine Sado-Masochistic frenzy with free-association imagery. The whole sound seems to be the product of a secrete marriage between Bob Dylan and the Marques De Sade." "The rock'n'roll music gets louder, the dancers get more frantic, and the lights start going on and off like crazy. And there are spotlights blinking in our eyes, and car horns beeping, and Gerard Malanga and the dancers are shaking like mad, and you don't think the noise can get any louder. and then it does, until there is one big rhythmic tidal wave of sound, pressing down around you, just impure enough so you can still get the beat; the audience, the dancers, the music and the movies, all of it fused together into one magnificent moment of hysteria." "Nico, astonishing - the macabre face - so beautifully resembles a momento mori, the marvelous deathlike voice coming from the lovely blond head."