His name was Shoer. Pronounced SHOO-er. He was a little robin (as in the bird, not as in Batman's friend). I called him Shoer because I was incredibly young and I thought he was a fish and I couldn't say the word "fish" and all I could manage was "shoer".
He was made of a cardboard tube, with some brown and red furry material stuck on to it. I think he had pipecleaners for legs, and he must have had a beak and some sort of face but I can't remember what they looked like. The cardboard tube was just the right size for my finger, so he was basically a little finger puppet.
And no, sadly, he doesn't still exist. I suspect he either went missing or possibly the materials from which he was constructed didn't survive. If he'd survived I'd have kept him because he was rather a wonderful little thing and I loved him. :-)
(OTOH, I do still have my teddy bear. That's lasted about as long as my sister has, IIRC, so he's about 40.)