Katheryn looks horribly misspelled to me. I like
Catherine and
Katherine.
Kathryn and
Katharine are acceptable too but
Katheryn just looks odd.
Emily Katherine and
Emilie Katherine.
I would actually prefer
Emily Catherine and
Emilie Catherine.
Catherine goes especially well with
Emilie, in my opinion, as
Emilie is French and we use
Catherine is
France too.