New Story Magazine started out in 1905 as Gunter’s Magazine, a Home Publishing venture. Following Gunter's death in 1908 the magazine was acquired by Street and Smith. In 1910 Chicago publisher, LaSalle bought the magazine and for its first issue (October) renamed it the New Magazine but with the old Gunter’s logo as a shadow behind the new name on the cover and contents page (elsewhere in the issue only the new title was used). The magazine's association Gunter effectively ended with that issue, volume 12 number 3. The very next issue restarted the numbering at volume 1 number 1, and dropped all mention of the former title.
In 1911, exactly a year later, LaSalle added 'Story' to the title. Although it remained the New Story Magazine after being re-purchased by Street and Smith in 1912 the name was changed one last time in 1915. The All Around Magazine continued as a Street and Smith publication until being closed down in 1917.
[Source: Galactic Central]