This could be The Foundling by D. M. Cornish (Goodreads || Amazon || Wikipedia)
Set in the world of the Half-Continent—a land of tri-corner hats and flintlock pistols—the Monster Blood Tattoo trilogy is a world of predatory monsters, chemical potions and surgically altered people. Foundling begins the journey of Rossamund, a boy with a girl’s name, who is just about to begin a dangerous life in the service of the Emperor. What starts as a simple journey is threatened by encounters with monsters—and people, who may be worse. Learning who to trust and who to fear is neither easy nor without its perils, and Rossamund must choose his path carefully.
So, it's a male character, but he has a "girl's name". Likewise, there is another character he meets named Europe:
At first I figured that this would be yet another boy-boy-boy book. But then you meet the character of Europe and it's all up in the air. Europe is the fighting fulgar that meets Rossamund early in his travels and inspires both his respect and his disgust. She kills monsters for a living, which wouldn't be so bad if the first one Rossamund encounters with her weren't such a sweet but stupid fellow.--Goodreads review
I got sidetracked and haven't finished the book, so I can only speak to the first part of it. The monsters all have names unique to the series, but I'm sure there could be a troll-like one. I don't recall any carriage incident, but it could certainly have happened in the later part of the book. The Wikipedia summary mentions an ettin attack and both a carriage and coach ride. Likewise, it says that Europe admits late in the book that she is "Europa, a duchess-in-waiting, set to one day rule over the rich city of Naimes".
I do recall extensive discussion of alchemical-type technology, as does this reviewer:
I was particularly enchanted by the world details that slipped into place; the complex, quasi-magical chemistry; the "vinegar seas" whose acidic waters gave sailors their rugged, pit-faced appearance; the boats powered by "gastrines," basically vat-grown muscles in large boxes.
Likewise, TV Tropes describes the series as
Combine Bio Punk and Dungeon Punk, mold it into a Coming-of-Age Story, layer in a lot of Lord of the Rings-style world building, and frost it with lots of alchemy, and you'll have the Monster Blood Tattoo series.
The plot starts with Rossamund being chosen from the orphanage to become a Lamplighter. He's told by his supervisor to go to the docks and meet a particular boat. He shows up in the fog and asks a boat captain he meets if the captain is who he is supposed to report to. The captain, a disreputable sort, tells him, "Yeah, sure, get on." and proceeds to essentially kidnap the boy. Not exactly a stowaway, but definitely shenanigans going on.
This reviewer has a good summary typed up, up until the boat:
The unfortunately (for him) named Rossamund Bookchild is an orphan. A foundling living in the charitable Marine Society, he lives daily with the torment of others jeering and physical blows from a particularly nasty fellow foundling Gosling. Though he is of age, he has been waiting long to be chosen for a life of service, for the Emperor of the Half-Continent, from the many trades coming to visit and choose their new employees. With his fascination for phamplets with daring exploits of monster killers, Rossamund's hearts desire is to be a vinegaroon, a sailor of the seas battling with aforementioned monsters.
His only sympathisers within the marine society are Master Fransitart, maid Verline and Crampaulin the dispensurist. Verline tends to him when the blows get too much. Crapaulin teaches the ways of potives (medicines). Of this Rossamund is an adept student, as inept as he is in other things such as Harundo, a fighting sport, being too small and meek to be of any threat to his foes. Fransitart has a hidden kindness for Rossamund. After one such duel with Gosling, Rossamund when visited by Fransitart discovers that his master has hidden secrets, has even killed a monster! He has a monster blood tattoo of proof but seems reluctant to show pride. Rossamund is confused and vows to find out more.
At long last the call come from a trade to interview Rossamund. The lamp lighter trade chooses him, to his dismay, this seemingly being one of boredom and lackluster living, no exciting brushes with monsters to look forward to.
He is readied with all the things needed for this new job and bundled off uncertain of his future before he can discover further secrets of monsters from Fransitart. And this is where his path takes a sideways turn. Instead of boarding the lamplighter boat, Rapunzil, he mistakenly boards the Hogshead, believing the lies of the pirate master Pounditch (corser - dealer in illegal goods). By the time he finds out it is too late.
Thus begins his unexpected adventure. Meek little Rossamund who dares not say no nor duck a blow, learns to fend for himself little by little, think a little shrewder and for once tries to escape his fate.
In his travels, he meets Europe, the famous Branden Rose (a female teratologist or fulgar whose job is to hunt and kill monsters) and her creepy evil Leer (servant). Together they have weird and wild adventures.
Rossamund discovers he has more to offer and also starts to question the moral rights and wrongs of killing monsters. Will he branded a sedorner (monster lover)?