Company of the Bloodoath. We actually swore a bloodoath to hunt down and kill and ancient red dragon who had bullyied and made us pay a magic item tax to live on evening. Spent a year and a half going on quest after quest to prepare for the battle.
My players' party name hailing all the way from the Akorros in the Republic of Darokin is Company-4-Hire, although recently the team has been torn apart.
One member has been lost, one has died, half of them are assisting the Harpers in a Sundering/Tyranny of Dragons storyline mesh, while the other half (including a cleric) are making their way to the Glantrian Principalities to consult with the wizards hoping to find a way to bring back their companions stranded in Toril. Things are very messy right now for Company-4-Hire.
A sample of recently generated names
Order of the Golden Bridge
Circle of the Flying Sharks
Eight Flames and a Mastadon
Companions of the Frosty Octopus
Questers of the Indigo Iguana
Children of the Happy Horses
Companions of the Burgundy Flames
Agents of the Sleeping Hero
Two Badgers and a Elk
Heroes of the Fell Ogre
Turtles of War
The long running group I play in is Phineas's Phreaks and Phantastical Beasts. P3B for short.
We travel the world looking for strange new acts for our 2 (soon to be 3) wildly successful carnivals and occasionally accidentally stop wars, cause dynasties to fall and prevent Armageddon from happening.
We are a Tiefling, Gnome, Dragonborn and Goliath.
The Knights of Noloknyr
Those Damned Elves (all elfin party who were declared local folk heroes to the commoners and outlaws/irritations for a tyrannical baron)
The Riders of WHEEEEEE!
...and <drumroll> The Steel Dragons [of Daenfrii].