William Evelyn Byrd, of Westover - Middle Name

I have been researching this line all day and night after discovering it's direct for my son on his paternal side.

I have not seen a single male in this particular branch with a middle name, much less it being Evelyn

This pdf file has excellent records on the names, marriages, etc. and this William is just listed as William Byrd I, his son as William Byrd II. I personally don't think they had the middle name Evelyn and that, noted, is a middle name used in another branch, the one that Rear Admiral Richard Byrd I is from.

http://ecctechservice.com/Byrds/Bird-Byrd%20Genealogy%20Book.pdf

Notice that the Wikipedia page doesn't use the middle name Evelyn for the males at this point:

https://en.wikipedia.org/wiki/William_Byrd_I

I think the confusion 'may' have come from the fact that Rear Admiral Richard Byrd IS a descendant of this particular William Byrd, BUT he's also a descendant from another Byrd branch that married into his line of descent. He actually is from a female descendant on this line, Evelyn Taylor (Byrd) Harrison, not a male descendant. However, Evelyn's daughter Anne Harrison married a Byrd and it's from that male line that Rear Admiral Richard Byrd is from.

The best I can make of it, the middle name Evelyn didn't begin to show up until Evelyn Taylor (Byrd) Harrison's daughter Anne (Harrison) Byrd's male descendants began using it, most likely to identify that their double-Byrd line stemmed from Evelyn Byrd on their maternal side.

This is Evelyn Taylor (Byrd) Harrison's profile. She is the only person I've found named Evelyn in her line (dismissing the middle name in her father, grandfather and great-grandfather's names that I believe have been eronneously added):

Evelyn Taylor Harrison

It's from her down her line that Evelyn as a middle name seems to hold up in documentation.

All that said, I certainly am open to being corrected if someone has documentation for the use of the middle name Evelyn for the male Byrds prior to the descendants of Evelyn Taylor (Byrd) Harrison. I just want to make sure I have my son's ancestors' names correct.

Thanks for any assistance and /or clarifcation.