Never curse your child with a name that they will spend their whole life spelling or correcting other people's mispronounciation of.
Jessamy is such a name, on both counts, as is my surname, which is why I know how annoying it is.
I don't know whether that's pronounced JESS-ah-me or Jess-AY-me. Other posters think JESS-ah-miy.
Every over-the-phone interaction where your daughter has to give her name will go:
Call centre droid: "And your first name?"
DD: "Jessamy, that's J E S S A M Y."
Because she will have learnt before she leaves secondary school that everyone will ask her to spell her name and she will resort to preemptively spelling it.
Why are so many people apparently allergic to names like Carol, Susan, Mary, Heather, Rose, or any of the dozens if not hundreds of available names that 100% of native English speakers know how to pronounce and spell? This is a child, not a car or a lifestyle accessory. She doesn't exist to demonstrate how kewl and yooniq her parents are.
Sometimes, I think that the countries that have an approved names list that you have to pick from have the right idea.