The first that springs to mind is Jenny.
Jenny is often elongated to Jenny Wren in the UK
A Jenny wren is actually a small song bird, correct name is the Wren.
Jenny, Jen, Jensta, Jenna, Ifer, Jenno, Jenna, J, JenJennyJenJenJen, Jenjen, JenniJenno(thats what my friends call me lol)
and here is a cool way to spell Jennifer: Jenni4
Jennifer Blushi goes by Jenny.
Jennifer Levinson goes by Jen.
Jennifer Dryden goes by Jenni.
Jennifer Ringley goes by Jennicam.
Jennifer Kreuser goes by Jenny.
Jennifer Kumiyama goes by Kumi.
Jennifer Kushnir goes by Jenny.
Jennifer Lipman goes by Bunny.
Jennifer Lax goes by Jenny.
Jennifer Rudin goes by Jennee.
Jennifer Samples goes by Jen.
Jennifer Rope goes by Jennie.