The extra "l" got into
Hillary back in medieval times. This is shown by the fact that the spelling with two l's seems to be the most common form for the
surname. Reaney &
Wilson's
A Dictionary of English Surnames has an example of a spelling with two l's back in 1275.
Since Americans are very familiar with surnames becoming given names, it was natural for many parents to think that
Hillary was a more appropriate spelling than
Hilary for the given name.
You have a parallel situation with
Alison. The most common spelling for this girl's name in the USA has been
Allison since 1963. And again,
Allison is also the more common spelling of the surname.