No matter how you spell it, Dar(r)ell or Dorrill (and Dorrell), apparently historically it was pronounced the same: as DORRILL, which is the phonetic spelling to the original pronunciation.

On joining Lincoln's Inn, London, to study law, John Harvey Darrell of Bermuda, who was to become its distinguished Chief Justice from 1737-1743, was asked by the Secretary...

..."who was somewhat of an antiquary, whether we usually pronounce the name DARRELL or DORRILL and I told him the latter, DORRILL, was a very common way of calling it in Bermuda. He enquired what were the family arms, and I told him according to the seal. He then said his wife, and elderly lady, was a cousin of the D. family (usually he said called DORRILL) then living at Maidstone in Kent, that they were Roman Catholics, and consequently excluded from Public Office at the time.

He was probably referring to the Darells of Calehill who were Catholic and had a chapel in the wing of the mansion."

[From "Darrell Notes" by Hon. John Harvey Darrell, Chief Justice of Bermuda.]

Thus, it appears that the ancient Darells of Calehill pronounced Darell as Dorrill, with the "a" having a phonetic spelling being close to "o". Nowadays however, most who use the Darrell spelling probably say the name as with the sound of an "a" most commonly heard before the "r" in "dare"

Dorrill (and Dorrell) is pronounced as if the "o" is an "a" as in the relatively long sound of "a" in "art" (and "dart", "darling"), "formed with the tongue muscles quite lax and with the lips more open than for any other vowels" (The Random House College Dictionary).

Nevertheless, a person's name belongs to them, and it is generally accepted that their pronunciation is the correct way for them and is the way to which they should be referred.