I think that Jessa could also be used as a nickname for Jessamine. Jessa seems to me a feminine name that is not as popular as other nicknames for Jessica - such as Jessie, Jessy, or Jess.
This just doesn't sound right. If you really like the sound, name your daughter Jessica, and call her Jessa if you wish. I personally think Jess and Jessie are much, much better nicknames for Jessica, this is just plain ugly.
My name is Jessica, and I always found it boring. But I adore the name Jessa, and think it would look great hyphenated like 'Jessa-Lee', 'Jessa-Rose', 'Jessa-Mae'. A girl in my class is named Jessa Mae, I think it's very pretty.
The use of "Jessa" as a full first name is incredibly juvenile and need I say it? Unattractive. As a nickname it stands on the thin line of neutral grounds... if that line is crossed to first, it immediately will receive my vote of childish, unprofessional, unintelligent, and ugly. This name is something that I like to call "forever young"... it will not make good transition into a woman's business career from childhood.
I disagree with Francesca, and there really is no need to be so incredibly rude about a name, for god's sakes. This name is not by any means ugly, let alone "forever young" I think it's a heck of a lot more mature sounding than all the Braden, Jayden, Aidan, Kylie, kaylee, Kayla, etc... Although it doesn't really seem like an actual name. I think it's a very refreshing and unique name compared to Jessica, personally :)