There are at least two bands using the name The Blue Hour:

1:
The Blue Hour are an indie band from Atlanta, Georgia with members Keith Vogelsong, Tracy Clark, Jon McAdam, Michael Bentley, Joey Arbuckle. They released the album I've Filled Up These Pages in 2002.

2:
The Blue Hour (at one time called The Dawn) was created in the summer of 1993 as the neo-folk/ambient project of Brian Hodges. Hodges incorporates voice, classical and acoustic guitars, flutes, tapes, programming, keyboards, mandolin, percussion and assorted noises. He has been aided by Christoph Gladis (12 string and electric guitars, additional programming), Zaac Aubrey (guitars, vocals, spirit) and Tom Moller (select percussion). Read more on Last.fm. User-contributed text is available under the Creative Commons By-SA License; additional terms may apply.