Also, can anything be done about 3-letter searches? Names like Iva, Ivy, Mia, etc. require a Google search. [A first-world problem I know.]
Unless there is some Xenforo add-on which solves this issue, there won't be anything they can do.
Xenforo's own website states that their search function will not work on any criteria less than 4 characters. vBulletin used to be the same way years ago, but something was eventually installed here to enable vBulletin to work on 3 character words.
I have my own issues with Xenforo's shitty search abilities and I found an add-on on Xenforo's website called Enhanced Search. I let Petra know about that add-on, but I don't know if Enhanced Search addresses the exact problem you mention.
I have noticed that you can sometimes work around the problem by using quote marks.
Madison Ivy returns 15 pages of results.
"Madison Ivy
" returns 3 pages of results.
The quote marks don't help out all the time, but it may help you in some cases.