Well, I suppose we do have to take into account of the various accents spoken around the UK at the time and of the ability of the enumerators to correctly transcribe what they thought they heard... I have an ancestor in my own tree whose name was Methuselah but he was transcribed once as Matthew Sellah.
I've had a poke about for Hawkins in the Wiltshire area and haven't come up with any sign of another Bina with the name Hawkins other than the one Carol found in 1981. What is surprising, to me at least, is that there are quite a few Binas for other surnames.... I think it must be a common shortening of Sabina/Sebina although I did find a Rhowbina birth register as well. There are some records of one Bina Stone (nee Tibbolds) who was occasionally shown as Abinah/Sabina. It must be a common shortening in Wiltshire and that's how it passed down to my Rose Bina.
Edited to add:
There is a 1851 record for an Abinah Tibbolds (1842, Wroughton, Wilts) with sister, Honos (1835, Wroughton, Wilts) and I would think the sister's name is Honor - which is a name found a couple of times as descendants of Job & Betty/Elizabeth Hawkins with one of their daughters named as such. The wife of these children is listed as having been born in Gloucestershire while the father is also Wroughton. Maybe one of them is connected to Job's wife and both Bina and Honor are names that come down through their family.
I know not to take too much notice of user-loaded trees out there but you can pick up some clues to be investigated further. On one such tree there was a claim (with precise dates!) of the marriage of Job Hawkins to his wife but on looking at the Pallots Index record attached the wife's name was Ann Giddings, not Betty/Elizabeth Giddings. Yes, she could have had two names but only used one for the marriage but I don't really consider it enough proof. However, what was interesting in looking into the Giddings surname is that there are two baptism records for someone called Giddings of the appropriate age to be the wife of Job Hawkins.
Elizabeth Giddings, bp 10/4/1805, Urchfont, Wilts. Father: Mark Mother: Elizabeth.
Betty Giddings, bp 22/2/1806, Urchfont, Wilts. Mother: Honor Giddings.
And lastly....
There is a Sabina Hawkins (b. 1866, Wilcot, Wilts) listed in 1881, Wilcot, Wilts., living with grandmother Elizabeth Hawkins (b. 1803, Urchfont, Wilts), which is the same village listed for the wife of Job Hawkins f/o William Hawkins. Not sure yet who she is the daughter of but it's an indication that the name Sabina had been used in the family prior to the birth of Rose Bina in 1888. Yes, I know I've just shown that there were two females born in Urchfont in the same era with basically the same name but the chances of both of them marrying a Hawkins is remote.... and there is a Pewsey death reg for a Job Hawkins in 1874 (aged 68) so William's supposed mother would have been a widow by then.
All very fascinating and just a tad frustrating...