Mythology, by its very nature, springs from the oral tradition and heritage of a population, tales which developed over time and retellings, encapsulating some portion of the truth into a wrapping of fantasy, religion, or confused nth-iteration retelling. It's no surprise to the scholar of mythology to find that there are several different versions of the same myth to be found depending on the location and point in its history that the myth is encountered. One such example of a myth with several variations is the myth of Prometheus, and one notable example is in the identity of the Titan's mother.
The most common name for his mother found among many sources (including Hesiod's Theogony) that Prometheus was the offspring of Iapetus the Titan and the nymph Clymene. There are other versions, albeit more obscure, which place the identity of his mother as belonging to the nymph Asia, who had the gift of prescience which she passed along to her son. In reality, as both of these nymphs are offspring of Ocean and Tethys, it most likely was a variation which sprang up based on location more than time, although owing to the second-hand nature of ancient mythology, it is probably nearly impossible to conduct this kind of research.
One curious item of note is that the mythology of Prometheus has been retained in current time, and lives on in many sources. Although noted authors like Ayn Rand, Shelley, and Lord Byron have continued to be inspird by Prometheus, there is a rather unlikely organization which has been in existence since 1956 that maintains an oral version of the mythology of Prometheus even to this day: the aptly named Order of Prometheus fraternity at Potsdam College in the State University of New York. According to their version of the mythology of Prometheus, the identity of Prometheus's mother was Asia, not Clymene. However, any attempt to trace a regression through the fraternal versions of the mythology will be even more frustrating since a new 'generation' of college students comes through once every two to three years, and twice a year with the inception of each pledge class, the myth is retold, and changes slightly with each oral transmission.
Therefore, after all is said and done, this is more a cautionary note to the casual observer of mythology than any sort of scholarly exposé. The minor details (and sometimes major outcomes) of ancient myths will vary from telling to telling. A difference of name, location, or order of occurrence doesn't invalidate one version of a myth over another, it merely serves to underscore the fluid and malleable nature that mythology has. With each retelling, with each transmission, a myth will grow and change to suit the needs of the generation which is experiencing its truths for the first time. As the name of Prometheus's mother exemplifies.
Greek and Roman Mythology
The myth of Prometheus