Arthur Dimmsdale's name tells the reader something of what Hawthorne's opinion--as the author--of this character is. The name Dimmesdale might be approached analytically from two directions. First though, the name Arthur carries associations with it.
Arthur is not a Biblical name. If Hawthorne had wanted to stress Dimmsdale's spiritual qualities, he may have chosen a name like Jonah or David or Micah or Daniel etc., depending on what spiritual quality he wished to emphasize. The best know association with Arthur is that of King Arthur in the legend of Camelot (there is now archaeological evidence linking the legendary Arthur with a true historic figure in England). King Arthur was noted for his courage, justice and valor.
The most obvious part of Dimmesdale is dim, indicating someone who is not so bright, not acting very much from a clear intelligence. This analysis of the name certainly fits Dimmesdale. It can be successfully argued with very little effort that his adultery with Hester was not in the least intelligent; it was very dim-witted behavior. Of lesser obviousness is the association with dimness of light and a countryside dale.
A dale is a valley, particularly a broad valley. Valleys are very often associated metaphorically and symbolically with low places in life, suffering, the low ebb of life, whereas high places such as hill tops are associated with strength and achievement and awakenings. By this reading, the name Dimmesdale represents the protracted suffering Arthur Dimmesdale puts himself through and endures as a self-administered retribution for his dim-witted behavior with Hester. Also the possessive sound ("Dimmes-") indicates that his dale of suffering is of his own making, which of course it is.
That Dimmesdale is coupled with Arthur indicates that his motive is not one of self destruction (such as self-inflicted wounds in today's society) but one of valorous reparation for his wrong actions. But again, since he is dim-witted as well as valorous, the reader can question his choices, which must, however, be weighed against the punishment he would incur if he were to publically confess.
Putting all this together, it can be said that an analysis of Arthur Dimmesdale's name indicates that, while Hawthorne is trying to emphasize the wrongness of Dimmesdale's behavior and the extremely highly questionable nature of his later choices, Hawthorne's opinion of Dimmesdale is that he is nonetheless a character of courage and valor with good intentions and heartfelt regret and remorse and that, even though he wronged Hester and himself, he truly wishes to atone for the wrong done. The sympathetic narrator's voice substantiates this analysis of Hawthorne's opinion of Arthur Dimmesdale.
Perhaps one of the points that Hawthorne is attempting to make through Dimmesdale's character is that a restrictive society and belief system, such as the Puritan society and belief system, leaves little or no room for true repentance that is open and public and therefore drives true atonement for wrongs committed underground, so to speak, into a dark dim valley of self reproach and reparation.