Rush were a Canadian progressive / hard rock band that have been known to heavily influence the progressive metal band Dream Theater. So much, in fact, that they have covered several songs from them, such as "Tears", "YYZ" and "A Passage to Bangkok", which have been played live on occasions (i.e, playing the song at the Toronto Massey Hall in 2004, respectively.)
It was also Drummer Mike Portnoy who came up with Dream Theater's original name, "Majesty", while waiting in line for tickets to a Rush concert, while they were also listening to the band on a Radio. He said that while the were listening to their classic song "Bastille Day", he commented around the conclusion of the song that their music was "majestic". It was then decided that they would go as Majesty.