Clark Kent is still Clark Kent, no Spanish name for him. However, most superheroes, villains and supporting characters have Spanish names like that.
So, just because, here is a list of the most notorious ones. I'll write in gray the most accurate they could have used instead (but didn't).
Superman / Clark Kent: Supermán / Clark Kent.
Batman / Bruce Wayne: Batman / Bruno Díaz.
Robin / Dick Grayson: Robin / Ricardo Tapia.
Wonder Woman / Diana Prince: Mujer Maravilla (o Marvila) / Diana Pérez. Diana Príncipe.
Wonder Girl / Donna Troy: Chica Maravilla / Dina Rosas. Dona Troya
Robin / Dick Grayson: Robin / Ricardo Tapia.
Wonder Woman / Diana Prince: Mujer Maravilla (o Marvila) / Diana Pérez. Diana Príncipe.
Wonder Girl / Donna Troy: Chica Maravilla / Dina Rosas. Dona Troya
Elongated Man / Ralph Dibny: Hombre Elástico / Rafael Rivas.
Sue Dibny: Susana Rivas.
Supergirl / Linda Lee: Superchica / Linda Lara.
Supergirl / Linda Lee: Superchica / Linda Lara.
Aquaman: Aquamán (can't recall if there was any translation for Arthur Curry, but it's likely Arturo something). Arturo Curi (although it would make him a Latin Lebanese).
Green Lantern / Hal Jordan: Linterna Verde / Raúl Jordán. Hal (Haroldo) Jordán.
Flash / Barry Allen: Flash / Bruno Alba. "Flushman" in Argentina (for some reason).
Kid Flash / Wally West: Flashito / Carlos Vela. Gualter Oeste.
Martian Manhunter / John Jones: Detective Marciano / Julio Jordán. Juán Juanez.
Hawkman / Carter Hall: Hombre Halcón / Carlos Lara. Carlos Salón.
Hawkwoman / Shiera Hall: Mujer Halcón / Mirna Lara.
Green Arrow / Oliver Queen: Flecha Verde / Oliverio Reyna.
Black Canary / Dinah Lance: Canario Negro / Diana Ríos. Dina Lanza.
Atom / Ray Palmer: Átomo / Ray Palmer. Raymundo "Ray" Palmera.
Adam Strange: Adán Luna. Adán Extraño.
Zatanna: Zitana. That one seems to makes no sense, as zitana is meaningless. Zatanna.
Batgirl / Barbara Gordon: Batichica / Bárbara Fierro.
Zatanna: Zitana. That one seems to makes no sense, as zitana is meaningless. Zatanna.
Batgirl / Barbara Gordon: Batichica / Bárbara Fierro.
Red Tornado / John Smith: Tornado Rojo / Juan Pérez.
Flash I / Jay Garrick: Flash / Jorge Forcada.
Firestorm / Ronnie Raymond: Antorcha / Ronnie Raymond. Ronaldo Raymundo.
Captain Marvel / Billy Batson: Capitán Maravilla / Memo Batson. Beto Basto.
Guy Gardner: Gil Garza. Gil Jardinero. (G and J sound alike in Spanish).
Mr. Miracle / Scott Free: Sr. Milagro / Oscar Liberal.
Starman: Astro.
Hourman: Horario.
Wildcat: Gato Montés.
Johnny Thunder: Juan Trueno.
Sandman: Arenero.
Guy Gardner: Gil Garza. Gil Jardinero. (G and J sound alike in Spanish).
Mr. Miracle / Scott Free: Sr. Milagro / Oscar Liberal.
Starman: Astro.
Hourman: Horario.
Wildcat: Gato Montés.
Johnny Thunder: Juan Trueno.
Sandman: Arenero.
Starfire: Nova.
Changeling: Mutante.
Raven: Corvina.
Darkseid: Oscuranto, Morbus or Penumbra.
Darkseid: Oscuranto, Morbus or Penumbra.
With Superman characters they tend to keep both names or at least the last one in English:
Lex Luthor: Lex Luthor.
Lois Lane: Luisa Lane.
Lois Lane: Luisa Lane.
Jimmy Olsen: Jaime Olsen. Jaime Olmos.
Perry White: Pedro White. Pedro Blanco.
Lana Lang: Lina Luna.
Pete Ross: Pedro Ross or Fernando Suárez.
Brainiac: Cerebro ("Brain"). Cerebrático.
Metallo: Metálico ("Metallic"). Metalo.
Parasite: Parásito.
Mr. Mxyzptlk: Senor Mxyzptlk (pronounced misleplik).
Bizarro: Bizarro (And "bizarro" is Spanish for "bizarre").
Krypto: Krypto.
Parasite: Parásito.
Mr. Mxyzptlk: Senor Mxyzptlk (pronounced misleplik).
Bizarro: Bizarro (And "bizarro" is Spanish for "bizarre").
Krypto: Krypto.
Batman characters:
Commissioner Gordon: Comisionado Fierro.
Catwoman: Gatúbela (close to "Catarella", like Vampirella or Barbarella).
Joker: Guasón or Arlequín.
Penguin: Pingüino.
Mr. Freeze: Capitán Frio (Somehow they gave him the name that should be used for the enemy of the Flash —sometimes they use "Señor Gélido", a better translation).
The Riddler: El Acertijo.
Egghead: Cascarón (meaning "Eggshell"). Cabeza de Huevo.
King Tut: Rey Tut.
King Tut: Rey Tut.
Gotham City: Ciudad Gótica.
Poison Ivy: Hiedra Venenosa, or Hortiga.
Two-Face: Dos Caras or Doble Cara ("Double Face").
The Ventriloquist / Scarface: Ventrílocuo / Cara Marcada.
Clayface: Cara de Barro.
Harley Quinn: Arlequín (sometimes Arly Quin).
Teams
Cities, places, and stuff
Gotham City: Ciudad Gótica ("Gothic City").
Metropolis: Metrópolis.
Krypton: Krytón or Kriptón.
Smallville: Villa Chica.
Coast City: Ciudad Costera.
The Watchtwer: La Atalaya.
The Batcave: La Baticueva (a made-up word).
Batmobile: Batimovil (another made-up word —since "bat" is "murciégalo", and that's too long, anything Batman-related is translated with the meaningless prefix "bati-", as in Batichica, Batibúmerang, Bati).
The Daily Planet: El Planeta ("The Planet").
Teams
Justice League of America: La Liga de la Justicia de América ("de América" is rarely said).
Justice Society of America: Los Defensores de la Justicia ("de América" is rarely said).
Doom Patrol: La Patrulla Salvadora o El Escuadron Suicida (that last one is "Suicide Squad", lol).
Justice Society of America: Los Defensores de la Justicia ("de América" is rarely said).
Doom Patrol: La Patrulla Salvadora o El Escuadron Suicida (that last one is "Suicide Squad", lol).
Teen Titans: Los Héroes Juveniles o Los Jóvenes Titanes. Los Adolescentes Titanes.
Wonder Twins: Gemelos Fantásticos.
Cities, places, and stuff
Gotham City: Ciudad Gótica ("Gothic City").
Metropolis: Metrópolis.
Krypton: Krytón or Kriptón.
Smallville: Villa Chica.
Coast City: Ciudad Costera.
The Watchtwer: La Atalaya.
The Batcave: La Baticueva (a made-up word).
Batmobile: Batimovil (another made-up word —since "bat" is "murciégalo", and that's too long, anything Batman-related is translated with the meaningless prefix "bati-", as in Batichica, Batibúmerang, Bati).
The Daily Planet: El Planeta ("The Planet").
Marvel:
Dr. Octopus: Dr. Pulpo.
Green Goblin: E Duende Verde. El Orco Verde.
Sandman: El Arenero.
Fatastic Four: Los Cuatro Fantásticos.
Mr. Fantastic / Reed Richards: Sr. Fantástico / Enrique Ricardo.
Invisible Woman / Sue Storm: La Mujer Invisible / Susana Sánchez.
Human Torch / Johnny Storm: La Antorcha Humana / Juan Sánchez.
The Thing / Ben Grimm: La Mole / Benito Gris. La Cosa.
Dr. Doom: Dr. Muerte. Dr. Perdición.
Galactus: Alberto el Hambriento (Hilarious! That means "Hungry Albert").
X-Men: La Patrulla-X, Los Hombres X ("X" or "equis" is a bit funny, because the word modern slang for "generic", "indifferent", or "it's ok").
Wolverine / Logan: Guepardo / Leonardo (keep in mind that "guepardo" is Spanish for cheetah). Also: Emilio Garra, Lobezno, Carcayú, Glotón, Aguja Dinámica ("Dynamic Needle") and Aullador ("howler"). Carcayu. Carcayú or glotón are the right way to call a wolverine (gulo gulo), and "lobezno" is only ok for a wolf pup).
Morpho: Morfo.
Professor X / Charles Xavier: Profesor X (the X is pronounced "equis") / Carlos Xavier (prounounced "ha•vee•er"). He is often called "Profesor Xavier" instead of Profesor X.
Magneto: Magneto (although "a magnet" is "un magneto" in Spanish).
Rogue / Titania. Pilla.
Daredevil: Dan Defensor ("Dan Defender"), or Diabólico (Diabolic). Tough one. Dan Defender is pretty bad, but the translation would be "Temerario", which has no D or anything to do with "devil".
Dr. Strange: Dr. Centella. Dr. Extraño.