Are both Name Taken and Jars of Clay American rock bands?
yes
Title: Jars of Clay
Passage: Jars of Clay is a Christian rock band from Nashville, Tennessee.  They met at Greenville College in Greenville, Illinois.
Title: Dan Haseltine
Passage: Daniel Paul "Dan" Haseltine (born January 12, 1973) is an American singer best known as lead vocalist for Christian alternative folk rock group Jars of Clay.  Haseltine has performed vocals, piano, accordion, percussion and most recently, melodica, while with Jars of Clay.  He has had different artistic titles, including songwriter, producer, film composer, music supervisor and art designer.
Title: Name Taken
Passage: Name Taken was an American rock band from Orange, California.  They were originally known as All That's Left in October 1999 until they discovered that the name was already taken; thus the name "Name Taken".  The band started in the eighth grade where they would play shows in their amphitheatre at lunch.  They later succeeded to record for such compilations as Atticus I and Warped Tour 2002.
Title: Music Builds Tour
Passage: The Music Builds Tour was a 23-show festival-style concert tour spanning three months in late 2008.  Rock bands Switchfoot and Robert Randolph and the Family Band, along with Third Day and Jars of Clay co-headlined the event.
Title: List of Christian rock bands
Passage: In the 1980s Christian rock started to become a staple in the music industry, fueled by bands such as Stryper. " Billboard" magazine started to post the top 10 Christian rock songs, and some radio stations started to play Christian rock.  Bands such as DC Talk, Newsboys, Jars of Clay, Audio Adrenaline and many others achieved commercial success.  This list excludes bands that are primarily heavy metal or hardcore punk; those bands appear in the list of Christian metal artists and list of Christian hardcore bands, respectively.
Title: Demons (band)
Passage: Demons are a punk rock/garage punk band from Sweden.  The band includes quotation marks in their name to differentiate themselves from other bands with a similar name.  Their music has been described as "punk 'n' roll", but the band claims it should only be described as high-energy rock.  Their musical style relies heavily on the energy derived from punk rock.  Influences include 1960s garage rock bands such as The Sonics, The Standells and Shadows of Knight, The Velvet Underground, The Stooges and New York Dolls; and punk rock bands such as The Damned, The Heartbreakers and The Saints; and early hardcore punk bands such as Black Flag, Bad Brains and Dead Kennedys.  "Demons" has often been compared to contemporary groups like New Bomb Turks, The Hellacopters and Electric Frankenstein.
Title: Hold On (Name Taken album)
Passage: Hold On is the debut (and ultimately final) studio album by American rock band Name Taken.  The album was produced by Saosin guitarist Beau Burchell.  The second track, "Hold on for Your Dearest Life", was subsequently collected on the "Warped Tour 2005 Tour Compilation".
Title: Haitian rock
Passage: Haitian rock, or rock kreyòl, started as rock n roll in Haiti in the early 1960s.  It was played by rock bands called "yeye" bands.  The name "yeye" derives from the Beatles lyrical verse, "yeah, yeah, yeah", which took off in the United States and was listened to by upper class Haitian families who had access to the radio.  Young Haitians formed small electric guitar-based bands.  These "yeye" rock bands were short-lived, as the addition of "compas" to their repertoires resulted in a sound was called mini-jazz, or "mini-djaz" in creole.
Title: G.a.s. Drummers
Passage: G.a.s. Drummers was a melodic hardcore band formed in Jerez de la Frontera, Spain at the end of 1997 by three teenagers who stood out from their other students due to their colourful hair dies and their taste in the california punk rock bands such as Bad Religion, Operation Ivy, NOFX, Lagwagon, The Descendents etc.  Original members from other small local bands Dani Llamas (guitar and vocals), Pakomoto (Bass and vocals) and Rafa Camison (Drums) started playing together and composing their own music and after one year of sending demos around the country they got put as the opening act for Swedish Punk Rock band Randy on their Spanish tour.  A tour that took the band through the whole country helping a lot of Spanish kids discover that there were actually Spanish bands capable of sounding as good as some of their favorite American bands.  This lead immediately the band to sign to a young record label called Slide Chorus Records a young emerging record label from Madrid which would start releasing albums for other Spanish Punk Rock bands.  This first release titled Proud To Be Nothing hit the streets at the end of 1999 and was presented on their first European tour which covered Spain, Great Britain, France and the Netherlands amongst Spanish punk rock legend[P.P.M.
Title: Once Just
Passage: Once Just is a three piece rock band with reggae, hip hop and punk influences, from Calgary, Alberta, Canada.  They were signed to an offshoot of Sudden Death Records from 2006 to 2009.  They requested a release from their label due to inadequate funding.  They are the only Canadian act to have played with Canada's Godfather of Punk (Joey "Shithead" Keithley) and Canada's Godfather of HipHop (MC Maestro Fresh Wes) Their album destination was produced by punk rock legend Joey "shithead" Keithley.  Once Just was previously called JUST, but changed names to avoid a legal dispute with a now defunct Southern California rock band of the same name.  Once Just first hit the national scene in Canada in 2004 when Much Music and Much Loud both picked up the video for the Once Just song "When It's Over", radio stations across Canada soon followed, and the song was a minor hit in Canada, hitting charts across the country.  In 2007 the song "Spin It" from the album Destination hit the top 20 Canadian rock tracks on Sirius satellite radio.  In 2008, Once Just played Junofest in Calgary for the 2008 Juno's.  In the past 5 years, Once Just has played over 500 shows in both Canada and the USA.  Once Just has played with such artists as, Jars of Clay, D.O.A. (band), Ill Scarlett, Marianas Trench (band), Rides Again, Staggered Crossing, MoBadAss, Maestro Fresh Wes, Danko Jones and many others.
Jars of Clay Name Taken