Lynata said:
The Regiment appears to be the primary organisational unit of the Imperial Guard - larger organisational groups are often depicted as being more ad-hoc, formed as and when a campaign requires, while Imperial worlds raise whole Regiments as discrete and permanent units, though the exact numbers of a given Regiment vary immensely (typically ranging from several hundred strong to tens of thousands of men).
In that regard, the use of the term "Regiment" to refer to a discrete part of the Imperial Guard seems entirely plausible regardless of their numbers.
As it stands, the notion of the Stormtroopers being of a single regiment seems to be a reference to the SAS, who themselves are a single Regiment within the British Army, and sets a standard for the quality of the Stormtrooper Regiment (and it seems appropriate to refer to them simply as The Regiment in the same vein as the SAS).
That aside, the numbers simply don't make sense given the scale of the Imperium - 10,000 men is less than nothing on the grand scale of things. The last informed estimate of the size of the Imperium I encountered (based on the number of worlds, and the approximate people per world all listed in the 3rd edition 40k rulebook) suggested a population of 3.3E+17. Even assuming that the total number of Imperial Guard is only 0.1%, that still means that there are thirty-three billion Imperial Guardsmen for every Stormtrooper. So few Imperial Guardsman would ever see a Stormtrooper that it's unlikely that they'd ever have been heard of by anyone, let alone have any sort of reputation.
And the problem with that is that if it took so rare a person to become a Stormtrooper (you'd need to sift through several worlds to find even one candidate), chances are The Regiment would never have been formed in the first place, in part because you'd normally never get enough of them together in one place in the first place, and in part because if they needed to be that awesome to start with, chances are they'd already have been taken by an Astartes Chapter (who, accounting for casualties suffered by aspirants, probably recruit more than 10,000 young men in total across the entire Imperium in every generation).
Frankly, if the Stormtrooper Regiment (or, for that matter, the Orders Militant of the Adepta Sororitas) were to actually have any impact upon the Imperium ever, a few tens of thousands of warriors is nowhere near enough (particularly not for the Sisters Militant, given that they're supposed to be policing the Ecclesiarchy, one of the largest and most widespread organisations in the entire Imperium... they're outnumbered by the Cardinals that command each and every Diocese in the Imperium). Frankly, my personal inclination is to ramp up those values by three or four orders of magnitude at least, within my own games anyway.
This is all personal preference; I'm working my way through planning an invasion of a fairly average world for my Deathwatch campaign, and 10,000 warriors would barely be a blip on the radar compared to the tens of millions of Guardsmen being deployed, and worse, there are so few Stormtroopers to go around that by those canon numbers, I cannot actually justify any worthwhile number of these elite troops... because in a Deathwatch campaign, anything that a single squad of Stormtroopers can do will be done much, much faster and more efficiently by a Deathwatch Kill-Team. It's far easier to justify two companies of Stormtroopers (about 600 of them in total for an entire planetary invasion) when there are 10,000,000 of them across the Imperium, rather than taking 6% of the Imperium's entire complement of Stormtroopers.


