There are many suggestions how to spell the name „Katherine“ correctly. During the 16th century, there was no rule as how you had to write your name. Without a set orthography, people were free to spell their names however they wanted to.
The name „Katherine“ is no exception. Even one of the most prominent bearers of this name, the well-educated Queen Katherine of Aragon, signed her letters as „Katherina“, „Katharine“ and „Katharina“. (And let's not forget the fact that her original name was Catalina.) Her first husband Arthur called her „Katerine“ in one of his letters, while her daughter Queen Mary spelled her name as „Kateryn“.
The case is very similar with Katherine Howard. In one surviving signature she calles herself „Katheryn“, but there also exist the versions „Catherine“ and „Kathryn“. It is therefore very hard to say which spelling is the „original“ one. Even though Kitty Howard signed as „Katheryn“ once, it doesn't mean she always did it. There simply was no orthographically fixed version.
But since there are so many versions – and so many Katherines in Tudor time – maybe it's time for another poll for Team Katherine Howard. If you guys favour a special version – soon you will be able to vote for it!