There are at least six artists named Ahab:

1) is a German funeral doom metal band, formed by members of Midnattsol and Endzeit. The classic novel "Moby Dick" by Herman Melville served as a source of inspiration for their music. They released an EP named The Oath in 2005 and a full-length album named The Call Of The Wretched Sea in 2006. On the artwork of the album, the style of the music is described as Nautik Funeral Doom. Second full length The Divinity of Oceans was released in 2009.
The Giant is based on E.A. Poe's novel "The Narrative of Arthur Gordon Pym of Nantucket" and was released in 2012 on Napalm Records.

2) is a German Noise-Rock Band featuring members of Ulme.
www.ulme-music.com

3) is a Danish band.
www.ahab.mymusic.dk
www.audiostreet.net/ahabdk
www.myspace.com/ahabdk

4) an Alternative Country/Folk band from London, UK. (see A.H.A.B.)
http://ahabofficial.com
www.myspace.com/ahabmyspace

5) Minimal 80s band from the UK

6) Glitch Hop / Bass Music producer from Texas.