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 Amy goes by Jen.
Jennifer Rudin goes by Jennee.
Jennifer Samples goes by Jen.
Jennifer Ringley goes by Jennicam.
Jennifer Rope goes by Jennie.
Jennifer Quirino goes by Thumper.
Jennifer Raine went by Poppet.
Jennifer Nee goes by JenNee.
Jennifer Nicholson goes by Jenny.
Jennifer Nitsch went by Jenny.
Jennifer Ogle goes by Jen.
Jennifer Ortega goes by Jenn.