I guess you guys are probably right! People sometimes shorten mine to 'Ell'. I've seen 'Iuv' on here (though I'm thinking that's not your real name). Tweety's real name i know, but it's not really abbreviatable.
Yes, Pet is, in part, a feminisation of my name. I was once widely known as Petal (some of my writings appeared under that name, and I'm still occasionally called that). Pet can be short for any variation on my name.
The mention of the Geordie use "Pet" may also be relevant. I used to be married to a Geordie.