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 Sky goes by Jen.
Jennifer Rudin goes by Jennee.
Jennifer Samples goes by Jen.
Jennifer Ringley goes by Jennicam.
Jennifer Rope goes by Jennie.
Jennifer Amy goes by Jen.
Jennifer Bancale goes by Starr.
Jennifer Blushi goes by Jenny.
Jennifer Bokobza goes by Gabou.
Jennifer Boutelle goes by JB.
Jennifer Bross goes by Jenny.
Jennifer Basa goes by Jenna.