In context, Jade is slightly less "filler" than Jane. This is coming from someone who likes Jade (and Jada) as a first name - it gets overlooked in the middle.
And Emily I find to be a rather boring name in its ubiquity.
That said... we're nerds here. There is, in truth, absolutely nothing objectionable about Emily Jade being someone's name.
Congratulations to your teacher on the little one!
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