This is an excellent question that required a bit of research, although ultimately, I'm not sure how answerable it is. The question presumes that the specific bass ostinato in question had a definite name (as is the case for the Folia and the Lamento, but which may not be the case here). However, we can at least try to trace the source of this motif.
Coincidentally, I was reminded of this question recently, when my Baroque Pandora station randomly happened to play Voglio di Vita Uscir, a madrigal attributed to Monteverdi which also uses this motif, but which strays from using it as a strict ostinato (though never far).
Side note: too late in my research process, I discovered an extensive page on the wiki that lists 17th century chaconnes, which gives a good feel for just how popular this form was, and provides a bibliography of names, dates, and pieces to cross-check.
As TangledUpInBlue suggests, the definition of Chaconne varied through history and by location. Indeed, that your particular bass line may have been considered, at least by some, as "the" Chaconne could be inferred by titles like Merula's "Aria sopra la ciaconna", or Giovanni Felice Sances' "Cantata a voce sopra la Ciaccona", both of which use the motif in the bass, and refer to themselves as being "over the Chaconne".
Plenty of online resources (including the wikipedia page) mention that the chaconne was likely imported, via Spain, from Latin America, where it was a highly provocative dance. If true, this might make it an early instance of Western music adopting African syncopation. It appears that keyboardists, lutenists, and guitarists first adapted the dance as a practice progression for improvising variations over. It seems there wasn't an exact specific progression that was being used, though they usually tended to follow a basic I-V-vi-V progression, possibly adding in-between chords, syncopations, or hemiolas.
According to "From Imitatio to Pronuntiato: Background, Analysis, Interpretation, and Performance of Antonio Bertali's Chiacona for Violin and Continuo" by Edith Hines (no relation):
In 1632, however, the situation changed with the publication of Claudio Monteverdi's Scherzi musicali: the collection included a duet, headed simply Ciaconna, with an unchanging bass line whose sharp melodic and rhythmic profile stood in stark contrast to the vaguely recognizable outlines of its precedents. Evidently "Zefiro torna, e di soavi accenti" made an immediate impression; as Alexander Silbiger observes, the years 1632-37 "saw the publication of a rash of vocal chaconnes, nearly twice as many as during the entire preceding history of the genre, almost all of which apear to imitate Monteverdi's example." He argues that "Zefiro torna" was, in fact, the prototype for all these pieces -- that "with this work Monteverdi established a new conception of the chaconne genre that was to be widely adopted." Indeed, within a decade the ciaconna was so well known that the poet Salvator Rossa could say, in a satire on Roman musical life, that "everyone is scandalized and bored by the singing of the Misserere to the Ciaccona."
So it seems that if any piece is to give it's name to this particlar bassline, it would be "Zefiro torna":
This idea is supported by the use of this motif in "Es steh Gott auf" (starting at 3:38), by the German composer Heinrich Schütz, who is known to have studied under Monteverdi in Venice about the same time that Zefiro was published.
Alexander Siblinger (the author cited in the above quote), has his article published as a chapter in Christopher Hogwood's book The Keyboard in the Baroque Era, where he also mentions an earlier chaconne that doesn't quite fit the Zefiro mold:
'Zefiro torna' was not the first published chaconne based on the unvaried repetition of a bass pattern; Manelli's 'Accesso mio core' is constructed on fourteen exact repetitions of the pitches C-G-A-G, the ultimate reduction of the chaconne bass, set out in equal note values. This slow-moving pattern provides, nevertheless, a suitable foundation for the lively interplay of the three voices, as they engage in points of canonic imitation and brief dialogs.
In another article by Siblinger, Passacaglia and Ciaccona: Genre Pairing and Ambiguity from Frescobaldi to Couperin, a bass line is described thusly: "The bass of the ciaccona, reminiscent of Monteverdi's well-known "Zefiro" ground, is treated more freely, although certain elements keep recurring."
I also found this blog post about Zefiro, where a commenter echoes the same statement about this piece probably being the source of the mid-Baroque Chaconne "fad".
On the other hand, there seems to have developed a more "refined" version of the Chaconne where there are fewer (or no) syncopations, and the chord progression is reduced to a simple descending tetrachord (similar to the Manelli piece mentioned above, but with the first V in first inversion).
This tetrachord motif can be seen clearly in this Chaconne by Lully, or (at times) in Correli's Chaconne, which doesn't really use a fixed bass ostinato.
Handel's Chaconne (a set of 62 variations from Suite 17 in G Major, HWV 442) takes this basic descending tetrachord pattern and extends it to an 8-note ground... Which quite clearly seems to have been the mold for Bach's Goldberg Variations -- a piece that I had never before realized was influenced by the Chaconne, though it seems obvious now.
Incidentally, the minor-key version of this descending tetrachord is another popular motif, often called the Lament Bass (which also had a chromatic version), and can also be traced back to Monteverdi, this time through Lamento della Ninfa (starting at 1:36). It's also commonly associated with Purcell's Dido's Lament, and Bach's Crucifixus. The historical relationship between Chaconnes, Laments, and the Blues is explored in much more depth by Alex Ross, here: http://www.therestisnoise.com/chacona/
As a parting note, after all this research, it seems that I can't escape the Chaconne... just today, Pandora played a movement from Biber's Violin Sonata 3 in F (starting at 4:57), which the score (on IMSLP) simply labels as "Variatio". But, of course I now instantly recognize it as having a Chaconne form, though based on Manelli's simpler ground (1-5-6-5), not Zefiro's.
