There are some names that sound ok as both full names and nicknames (like Lucy), but I generally don't prefer nicknames as full names.
Of course, it is your baby and you should do what you like. I do think it is important to acknowledge that there is a class bias against nns as full names in the US. That is, historically, the use of a traditional nickname like Jack or Molly as a given name has been a marker of low social status (or slavery). I think that is fading a bit in recent decades, but it is still there. The classic example is William Jefferson Clinton vs. Johnny Reid Edwards — Bill Clinton had the formal name and could position himself as Bill when he wanted to portray a folksy persona, but John Edwards changed his name to John because Johnny was not the name he wanted for his professional career.
That doesn't mean that there are no lawyers named Jenny and no doctors named Matt. Of course there are. But the class bias does still exist. That's not a reason not to use the name you love, but it is one factor to consider.
And I totally agree w/ pp that Jacob Edward would make me think you were a Twilight fangirl who couldn't pick a team!