If we go by the lines of the OP, my signature pokemon was a dragonite/mewtwo hybrid that was a cause of a GSC glitch (not intended) that I had nicknamed Devil, and it decimated the other kids I was affiliated with at school, neighbourhood, and camping site.
So yeah, I was known for it. Though I was mostly known not for a pokemon, but for a move. .... It wass the infamous Double Team, the seed of cringe and dismay. Most of my mons had it. Now that I reminiscense, I might have been a pretty annoying poke-kid >,>
But such a thing as a hybrid does not legally exist, and a move is not a signature pokemon, so it's story time:
Once upon a time, during my first gold playthrough, the time came for me to battle jasmine. After a couple of unimpressive generic Magnemites (sorry Viri) she unleashes a metallic creature of terrifying and cool design, leaving my kid mind speechless in awe. And then I heard its regal roar. The pixelous sound filled my ears, confirming the supposed size and ferocity of my opponent, and awoke in me the first doubts about the outcome of the fight. They also awoke a flame of desire inside me. "I want this beast" I thought.
It was much later, in Silver Cave, where I met a golden onix. I immediately caught it with one of my cloned masterballs that everyone had those days.
In a week I was drooling over my lvl 100 golden Steelix sprite, and it was grinning back at me. I was actively using it in battles, earning a good amount of Snorlax frowns. Never got as known as Devil though. Only I knew that it was my favorite mon.
And it still is. After so many years and generations, my liking for Steelix is as Sturdy as the behemoth itself (pun-seption intended).
It is ATM the mega pokemon of my "fav mons team" which I created after the loss of all my other showdown teams after a chrome reinstall (I lacked foresight :/) and kicks clefable asses.
Many others have come close but not earned the #1 spot, most notable being umbreon, glaceon, and dragalge.
According to the OP I need a picture. Just look at my signature then! ( wait, that actually makes it my "signature" pokemon. HA!)