Elsewhere I've tried to explain how the original form of Vaughn/Vaughan in Welsh was "Fychan" pronounced with two syllables, something like "VAH[CH]-uhn."
There is an even odder spelling of the name that appears on rare occasion, "Vaughham." We find it on Eleanor's Patriarchal Blessing given in 1856 by Patriarch John Young, Jr., brother to Brigham Young. It was Cousin Judy Vaughan Atwood who found it because my first attempt to request the blessing from the Church History Library failed as the spelling was so far off. Judy got it and then I just confirmed with my own request using the odd spelling.
It's clearly her because everything else is a match. It was given in November 1856 a few days after she received her own Temple ordinances in the Endowment House. Her birth date is given as 25 December, 1880  with birthplace as Whitney, Herefordshire, England, and parents, William and Jane Jenkins.
Vaughn was not a common name in Utah Territory. The 1856 Territorial Census shows three Vaughan or Vaughn families, one in Salt Lake City 8th Ward, one in Pleasant Grove, Utah County, and one in Cedar County, a former county on the west side of Utah Lake. There is also a miscellaneous Manifred Vaughn in Weber County. None of these people appear to be related to us. And oddly, they don't show up in the 1860 federal census for Utah Territory although there are three miscellaneous male Vaughns in Carson County, Utah which soon became part of Nevada. Two of them were in Virginia City and one actually a lawyer in Jacks Valley, of all places. None of them seem to be related to us.
It is my opinion that "Vaughham" is based on the old Welsh pronunciation of the name with two syllables. There is an audio recording of three individuals attempting to pronounce this spelling of the surname at: https://www.howtopronounce.com/vaughham/.
My guess is that Eleanor gave her own name verbally; neither Patriarch Young nor the recorder were familiar with the name and the clerk attempted to write it like they heard it. I think in that misspelling we have a pretty clear indication of how Eleanor spoke English with a Welsh accent.
Oh, and if anyone in the family wants a copy of the blessing, Judy and I are glad to share it. Or you can get it from the Church History Library. They always come with the reminder that they are sacred and not to be widely shared outside of close family.