This group released as the American Quartet on Victor releases, as the Premier Quartet on Edison releases, and as the Premier American Quartet on releases by Emerson. Pathé releases used the name Premier American Male Quartet. Columbia used both the Premier American Quartet and American Quartet names. Okeh releases used the American Quartet name. Aeolian-Vocalion used both Premier American Quartet and the Murray Quartet. Edison releases appeared for this group using both the "Premier Quartet" and the "Premier Quartette".
Via contracts with Billy Murray, they were contracted to Edison for cylinder releases only, while also contracted to Victor for disc releases only, but each contract using the different name for the group. In 1914, Edison and Victor worked out an agreement regarding Billy Murray's contract, such that Edison also would be allowed to release discs with Billy Murray as a member of the Premier Quartet.
In July 1920, the members of the Peerless Quartet (which shared some of the same members as the first group), Billy Murray, and Henry Burr together signed an exclusive contract with Victor Records. With Murray now exclusive to Victor, the version of this group which recorded for Victor split from the version of this group which recorded for Edison, such that the American Quartet and the Premier Quartet were no longer the same group.
The post-split Premier Quartet released on other labels as the Harmonizers and as the Harmonizers Quartet.