I too have been trying to trace the origin of the name, Howarth.
The Haworth Association of America site at http://www.haworthassociation.org/toc.htmhttp://www.haworthassociation.org/toc.htm appears to have been around since about 1900. Within the site index is an "Origins" page at http://www.haworthassociation.org/name_origin.htmhttp://www.haworthassociation.org/name_origin.htm
The author of the origin paper, James M. Knox, provides a fairly long list of credible references. The text refers to various derivations or derivatives of the name Haworth, for example, HEYWORTH, HEAWORTH, HAYWORTH, HOWORTH, HAWORT, HAWORD, and more ancient spellings such as HAUWYRE, HAUWRTHE, HAUOORTHE, HAWURTH, HOUWORTH, HAUWORTH.
Mr. Knox also refers to the more modern spelling, Howarth, although he doesn't go on to explain the "when" or the "why". This, unfortunately, appears to be one of our missing links. As for the meaning of Howarth vs Haworth, you will find one possible answer in Message 90 of this board. But, although "Hoh" and "Haw" may have distinctly different meanings, one cannot conclude, on this basis, that the two names do not originate from the same ancient source, which may be HAUWYRE, HAUWRTHE, HAUOORTHE, HAWURTH, HOUWORTH, HAUWORTH or something similar.
To this list I would also add other names that I have encountered and result from replacing an "a" by an "e", an "o" by an "e", or vice-versa (e.g., Heywerth, Haywerth, Howerth). And then, I have also come across these names with a "y" added to the end.
To the above, I will add my own musings, but I hasten to add that I have yet to research in any detail. So, I may very well be off-base.
When you mentioned "the Anglos", were you perhaps referring to the Angles? It was this tribe that settled in the whole area north of the Humber (Northumbria), although perhaps only the east side. If the name Haworth or Howarth originated from this tribe, however, then the name would be of North German and/or Danish origin. Although Northumberia may not have included the Lancashire area, inter-relations between the Britons and this tribe would have developed over the years and so the propogation of the name in various forms would begin to appear and spread. But, of course, this would not explain the apparent beginnings and concentration in the Rochdale area.
I am also curious to know why you think the name cannot originate from the Danes (or Vikings, Scandinavians, in general). Some maps of the area of the Danelaw that I have seen do include Lancashire or parts of it. Within Lancashire, there are several place-names, reputed to be of Dane or Viking origin (e.g. Oswaldwhistle, Irby, Kirkby, Ormskirk). The Vikings (Danes) appear to have assimilated into Britain with "relative ease"; and consequently, language and culture in the area, north of the Humber, became a mixture of the Britons, Angles and Danes. In this same period, the Irish/Norse Vikings established settlements in Cumbria and along the Lancashire coast. Even if the Norse or Dane Vikings did not actually settle in Lancashire, the area was flanked on all sides by their influences and therefore I would be unwilling to dismiss the possibility of Dane origin too quickly. It's unfortunate that historians have to rely heavily on the Anglo-Saxon Chronicles, written by those living south of the Humber, as the Chronicles don't dwell on the social development of this region.
The Danes are also known to have invaded and colonized Northern France and mixed with the existing Normans. But even if the Normans that came to England were of Norman-Dane origin, they likely did not bring the name Haworth with them; otherwise, we would see evidence in Normandy. It is only speculation,but the appearance of Robert de Haworth, Henry de Haworth, etc., in England in the 13th century are Anglo-Norman combinations, the place-name being adopted by William I's nobles when they were granted titles in the Lancashire/Yorkshire area following the 1066 conquest. Hence, the name existed before the arrival of the Normans.
This only takes me back to a Briton, Angle or Danish origin, which is where I started in the first place.
Please correct me on any of this. I am only just starting out from 3000 miles away (Canada), so I am somewhat limited in readily available resources.