I've only ever had 4 different names here, so a small run-down on the inspiration for each of them
Soulflame Ninetales (oldest) - This is a common one I use over the net. It stems back from the days of playing my Gold Version from a Flareon I had called Soulflame. I really liked it (Zap Cannon 4tw!) and was impressed with its strength so I named myself online after it. The Ninetales part came from Ninetales being overall my favourite pokemon, eventually I named every Ninetales I trained up "Soulflame" while now any Flareon I train is named "Pyrus". Hmmm...I could do Pyrus Soulflame :D
I, Riolu & I, Lucario - A play on title of the movie "I, Robot" which in my opinion was a very good movie and the title of somebodies fiction on fanfiction.net called "I, Flareon" Originally I was just to be I, Lucario and not use I, Riolu but I changed my mind because I liked the idea of changing my name as a reflect of a pokemons life and how it changes upon evolution.
Crimson Arcanine - Couple of reasons, we'll start with the Arcanine bit. Many would conclude that Vulpix and Ninetales have always been my favourite pokemon. This in fact was not true, once upon a time back before I even had a gameboy, my favourite pokemon was actually growlithe. I promised myself when I got my first game I would find a growlithe and train it up, I got blue and went through the game...to find...there was no Growlithe! Instead there was Vulpix, which at first I disregarded and thought was girly looking. But eventually after restarting my game I caught a Vulpix giving it the name Vicki. In that same game, I'd found my love of Sandshrew and Raticate was a often used pokemon choice for me (I used a Bubblecate, termed by me because of the usage of the move Bubblebeam).
On that same game, I had what have only ever had three times (the others with Lucario in the Elite 4 on Pearl and Jolteon in a 3 on 6 battle with a friend on Blue Version, where I knocked out 5 pokemon with just Jolteon and yes I had 3 pokemon). Simply I was going to Fuschia City from Lavender Town, and I'd just worked out that I should of packed more healing items. I was down to just one poisoned pokemon on low health so I began to search for SOMETHING that would allow me to make it to Fuschia City without blacking out and having to go from Lavender Town again. Then I noticed the firestone, earlier I had tried to train up my vulpix against the trainers back along the road and had succeeded to reach a level where it had just learnt Flamethrower, but it just didn't have the power to beat up the tougher flying pokemon in the area. I was loathe to evolve my Vulpix but did so. My first real glimpse of my new Ninetales impressed me and noticing now that using the stone on it have gave it some more HP, bringing it out of being fainted. What would happen on my struggle through the remaining trainers was something that would forever knock off Growlithe and Arcanine as my favourite pokemon. My poisoned pokemon had fainted and I was left with a Ninetales on 17 HP as the only pokemon left in action did not leave me with much confidence that I was going to make it....but 10 minutes later I'd made it safely to Fuschia City, destroying any trainer in my way, with a Ninetales on 11 HP.
From then on it was Vulpix and Ninetales not Growlithe and Arcanine that were my favorite pokemon. I eventually got to get a Growlithe only after I got my Yellow version but it never do as well as my Vulpix did even after it evolved. Interesting to note that none of them appeared on what I consider to be the most successful team I ever managed to make (I termed them the Legends because of some of their successes), In Gold I faced a similar problem as in Blue but on the other foot. Sadly, I ditched Growlithe for Houndour and it never got its chance to complete for its lost title.
Gold saw the only time I used both Arcanine and Ninetales but was not impressed with either. After a decade Arcanine has finally started to challenge Ninetales in that position for my most favourite pokemon. The Ninetales I train on Pearl was rushed and of a poor nature, while the Arcanine I have is the closest thing to a truly competitive pokemon I've ever trained, and although Ninetales has lasting power and hypnosis, my Arcanine's high damage potential and speed on a team that really isn't too fast has knocked out my Ninetales out of my semi-competitive team, So I decided to honour my first true favourite pokemon and one that has always seemed to be overshadowed by a fellow Fire type. It may also be a glimpse into the future, where Arcanine will be my favourite pokemon of all, rather than Ninetales...but time will tell
And finally the Crimson part comes from the only one of two organisation I "made" in games which actually went anywhere known as "Crimson Reign Syndicate". the other one was "Sanctus Tempum" a corporation in the game Eve Online I created, owned and ran for six months before it finally died. The two reasons I didn't use that as my basis where that it was catchy enough and I didn't want to step on the toes of a certain other PC member.
TLDR version - The name is a tribute to a pokemon I really should have given a chance a long time ago.