One of my relatives spells her name in hebrew – kuf, yud, lamed, heh (KAYLA). I was told that this is the wrong spelling and it should have two yuds and end with an ayin instead of a heh. My relative says that this is how others spell it and she doesn’t want to change it. If this spelling is used on her kesuva one day, is it a problem? Thank you.
No, this is no problem, and she doesn’t have to change the spelling of her name.
Although it is true that some spell this name as you note, and others spell it Kuf Yud Yud Lamed Hei or Alef, it is okay for your relative to spell her as she wishes, and it is true that many spell it as she writes (though this is rendered Keala in English).
This won’t present any problem for the Kesubah, and if there’s a need (chalilah) for a Get then the dayanim will work it out.