Expanding on my comments above:
(Caveat: I haven't done any recent reading of canonical sources. If you catch me misrepresenting canon, I'll accept correction.)
I see the Naval Regiment as multifaceted.
A. First, and most common, Naval Regiment is a training-and-qualification activity for individual IN service members. (The availability of this training for non-IN personnel is possible. Subsector and planetary naval personnel are likely; megacorp merchant personnel are less likely but not beyond the pale.) This qualification would be more common in some branches than in others. In rough descending order of frequency (Using IN branches from CT High Guard '80):
1. Gunnery
2. Crew/Line
3. Engineering
4. Technical and Medical
5. Flight
Comments on A:
1. I'm not sure if Crew/Line would be closer to Gunnery or Engineering in terms of frequency.
2. Naval Regiment qualification might well be a plus for promotion and command assignments for Line officers at a level of priority beneath the game's level of granularity.
3. Technical and Medical are "too close to call" in terms of relative frequency.
4. Naval Regiment-qualified Flight officers would likely be "player-character rare" (he said intentionally
), or close to it.
B. Second would be Naval Regiment units assigned to IN bases, depots, and other facilities. These would provide security and basic naval law enforcement, as well as defensive action in the event of a personnel assault on the facility.
Comments on B: similarities to U.S. Navy Shore Patrol are clear. This function needs to be performed by someone; if not the Marines, then the Naval Regiment is the obvious choice. Splitting the duties, using IN personnel for routine security and law enforcement and Marines for defense, is another possibility. In a politically charged 3I (or area thereof), a separate organization might even be employed for the routine work.
C. Third would be Naval Regiment units assigned as Ship's Troops. The rarity of this kind of unit is due to two factors: the far more common use of Imperial Marine units as Ship's Troops, and the general policy for ships lacking a Marine unit as Ship's Troops to use Naval Regiment qualified crewmembers as ad-hoc boarding parties; this policy is a major driver of the first facet above.
Comments on C: I could see Naval Regiment particularly used in this role on IN transports for Marine units. This eliminates double-tasking of the Marine contingent, freeing up their time for mission preparation, and also eliminates any possible conflicts between the Marine contingent and Marine Ship's Troops.
D. Last would be the Naval Regiment units that exist specifically as ground troops. These do exist, usually due to history and legacy, and are trained and equipped for that mission. Here, I don't see them as heavily invested in meteoric assault as the Marines, but rather making use of high-G landing craft as their primary deployment method. I am inclined to see an even higher use of Battle Dress, up to and including these units being 100% Battle Dress.
Comments on D: The existence of such units is canonical. I do not recall the canonicity of their deployment methods or equippage.
In the context of the above, the existence of an IN special operations unit, under the auspices of the Naval Regiment, is reasonable (though certainly not inevitable). An obvious prerequisite for selection for such a unit would be Naval Regiment qualification, though that qualification could be gained in the initial training for the special operations unit by personnel otherwise suitable and desirable. If cross-service recruiting is occurring, equivalent qualifications from other services would likely be acceptable.
I would see such a unit as smaller in total personnel size than the Marine Commandos, with a distinct mission profile. Their missions would likely be driven by and in support of IN mission priorities, sometimes (often?) in close cooperation with IN Intelligence (even if the latter has their own Operations unit; redundancy is not always wasteful and cooperation can benefit all parties).
Where the above contradicts canon, I am of course in error. Where canon is silent on the above, the above is interpretation and speculation; Your Mileage (and preferences) May Vary.
Commando operations call for multi force cooperation and the SEAL team concept is one that will probably carry forward for a long time. And the SEALs pull Naval personnel from all sorts of venues. Since every Marine is an infantryman, that distinction isn't so much a factor.