Well when it comes to naming my own mechs, nothing short of a name with a lengthy history and deep meaning befits every mech. To me, a name must mean something. It must have depth. For naming a mech will give it more than a simple nickname, it will give it a close personal bond between pilot and mech... And that is what True Mechwarriors are all about.
For an example my AWS-9M has the name "Quandary". It took a lot of thought before I decided to buy it, It took so much more thought to make it a viable mech and I still cannot possibly think up any good reasons why it plays well or why I'm somewhat infatuated with it.
I named my 3 phoenix variant mediums after the 3 wisemen. Balthazar, Melchior, Gaspar. The shadowhawk, the Griffon, the wolverine.
My HGN 732 is named "Prodigal son". Seeing as I've sold and re-bought it over 4 times now. Lore wise with my rp character, this specific mech is always hedged on notorious bets and gambled away, only to mysteriously and annoyingly return to my possession at the strangest times.
I named my centurions after chess pieces, to reflect their play style and strategy. As well as their hierarchy status in my medium kingdom.
Yen lo Wang ~ "King" he might seem to have limited potential but he is always underestimated.
CN9-A ~ "Rook" Solid, straight forward, does not cut corners. When the Rook takes on an atlas, he does not falter.
My founder's Atlas carries the name: "Nemesis".
Were he to turn against me, I shall have met my true arch enemy. There's always a ton of Ac20 ammo stored in the head compartment, regardless if he's carrying an Ac20... In my character's rp, the shells are hollowed out to make room for a small bunk house, in which I live.
Another one of my favorites is the Stalker 5S which I promptly named: the "Mastodon". The original design centered around 6 small lasers and 4 srm 4's. Biggest engine and 22 double heat sinks. Once the Mastodon got you in charging range, it followed one path and that is straight through your burning wreckage of a mech.