Prior to its renaming to Thor, the title was originally Journey into Mystery. Thor had first appeared in #83 of that series and quickly became its starring character. Although the front cover had depicted "Journey into Mystery with Thor" the title did not offically change names until #126.
Throughout its series, the adjective "the Mighty" preceeded Thor. While the indicia reflected this for long periods of time, it was inconsistent. For the sake of simplicity, this site considers this series simply to be "Thor" and the title explicitly named "Mighty Thor" in 2011 to be the first series of that name.
Following the Onslaught crossover and the beginning of the Heroes Reborn event, the title reverted to Journey into Mystery, with other Asgardians being the stars of the series. When the Heroes Return storyline began a year after the renaming of the series, Thor returned to his own title, the second series to bear that name.