There have been multiple groups that have used this name. 

1) Undercover was a Hard Rock/AOR group by a ex-Vandenberg singer Bert Heerink from Netherlands who make 2 albums in the 90s. One was Undercover (1990), a cover album, and second record was All Line Up (1994).

Personnel:
Bert Heerink Vocals
Dick Kemper Bass, Vocals
Ronald Bekking Guitars, Vocals
Ivo Elfers Drums
Cyril Whistler Guitar, Vocals

2) Undercover was a UK based pop-house group who hit the UK #2 spot in 1992 with their Stock, Aitken, Waterman produced cover of Baker Street. Pop covers of Never Let Her Slip Away and I Wanna Stay With You followed before the demise of the S/A/W 'Hit Factory,' but by then, Undercover's star was starting to fade anyway.  They released two studio albums, Check Out the Groove and Ain't No Stoppin' Us!. 

3) Undercover was one of the pioneering acts in Christian music. Formed in the early 1980s by Joey "Ojo" Taylor in southern California, Undercover brought a new punk sound to the Contemporary Christian music scene that differed from the Christian rock and Christian metal bands of the time. Through more than two decades and a few lineup changes, the band released eight studio albums and two live albums, and is considered by many to be pioneers in what would later be called Alternative music in the Christian world.

While the band has seen several members come and go (and come again), Taylor has said on more than one occasion that the band decided sometime after 1994's Forum that "Undercover is Ojo, Gym, Sim, and Gary," emphasizing that any other lineup, if any, would in the future be called something else.

Undercover played two reunion shows in California in August 2005.  Their first eight albums have been collected into two sets, Anthology 1 (the first four albums on two CDs), and Anthology 2 (the next four albums on four CDs).

Original releases
Undercover. 1982, MRS Records.God Rules. 1983, A&S Records.Boys and Girls Renounce the World. 1984, A&S Records.Branded. 1986, Blue Collar Records.3-28-87 (live album). 1988, Broken Records.Balance of Power. 1990, Broken Records.Devotion. 1992, Brainstorm Artists International.Forum  1994, WAL.Live at Cornerstone 2000. 2000, Millennium 8.I Rose Falling. 2002, Galaxy21 Music. 
Re-releases and anthologies
 Volume 1 (compilation of Undercover and God Rules). 1988, Broken Records.
Volume 2 (compilation of Boys and Girls Renounce the World and Branded). 1988, Broken Records.
Anthology Volume 1 (compilation of first four original releases). 1996, Innocent Media.
Anthology Volume 2 (compilation of next four original releases). 1997, Innocent Media.
Cornerstone 2000 (re-release). 2002, Galaxy21 Music. 

4) A Japanese band that changed their name to C-999 in 2004. Please tag them as ｕｎｄｅｒｃｏｖｅｒ.

5) A Denver band that was well known for playing covers and has branched into creating their own music.  The band is led by two sisters.