Her concept would make a good Rogue-9 (Assassin) with the perfect disguise ability they get then. I don't like the non-Monk-Monk "don't tell me what my PC is like!" thing, though. Personally as GM this is a good example of why I don't use the 5e optional multiclassing rule, there is too much of a clash of expectations around what it means to be Monk class - is it purely mechanics crunch (as you seem to think) or does it say something about your character's role in the world. I don't want to be constantly doing a double-take "Oh yeah she's a Monk, only not really..."
She's
not a monk, in terms of studying at a monastery. She was taught deadly unarmed combat techniques; think special forces/commando/Jason Bourne.
And this is the point re: this thread. The classes are not 'real' in the game world. A person can certainly be a 'monk', think of themselves as a monk and call themselves a monk, but that would mean that they studied at a monastery, not that they were experts at unarmed combat.
In world descriptions/titles may or may not be the same words as the name of a game-mechanic character class, but if you introduce yourself as a 'fighter', they may believe that you, er, are good at fighting, but there's no way they'll think, 'Ah, you must be able to heal yourself once per hour, then!'
What you said earlier about the body language of veterans: this is true to a greater or lesser extent, but there's no way that every NPC on the planet is an expert in body language!
For 'adventurer', that may be applied (as a pejorative) to those who act recklessly, but it is a result of how you've behaved, not something intrinsic to you (like your race), and not something that every Tom, Dick or Harry can tell by looking. Although it's most often the Dicks...
One of the things I like about multi-classing is that it makes it easier to avoid other people's imposed stereotypes based on game mechanics that creatures in the game world cannot possibly know.
As for, 'Oh yeah, she's a monk but not really'....No! They have absolutely no reason to think 'monk' at all! Therefore,
not being a monk isn't a difficult concept.
It's the unearned stereotype I hate. If a person sees me smashing someone's nose with my elbow, this should not give them the (erroneous) belief that I was raised in a monastery!
The 'expectations of what it means to be a monk class': whose expectations? Creatures in the world? They have no concept of the game mechanics of 'class & level', so they have no expectation that those who can kick someone's teeth out must have been raised in a monastery or any other 'monk' stereotype. Expectations of the players? My legal character can do exactly what its game mechanics say it can, and it's wrong for other players or DMs to tell me that my characterisation must live up to their stereotypes.