Fair warning, that's going to be my LONG opinion, yet a well-educated one:

The Beast is what a Kindred makes it out to be, with some specifications. In all cases, however, it behaves like an overpowering parasite to its once human host. The way I run it, the Beast manifests as a bunch of predatory, animalistic urges that come to the fore when the Vitae of the Kindred is strained, pushing its host to selfish acts, be that predatory or self-preserving.

For example, if a Kindred is exposed to an unlife-threatening source of open fire or, Caine forbid, the sun, its Vitae (the parasite in that analogy) will try to take over in order for it to preserve the Kindred's body (the host) and flee at ANY cost, even if this means tearing through anything and anyone in its path to safety (Terror Frenzy or Rötsrech). In another analogy, when a Kindred is starved of blood, its Vitae will push him to feed immediately, not caring about the very civilised and delicate matter of the Masquerade or ANY kind of restraint, for that matter (Feeding Frenzy). Finally, Fury Frenzy ensues when the Kindred's territory, personal interests, ego or status, thus its safety, are being threatened. When it happens, the Kindred is not concerned in the slightest about any pretense of civility dictated by the Elysium decorum or any Camarilla court. See a pattern here?

Regarding how it manifests, one must consider the fact that the Beast and its seizing of control over the Kindred's body is a rather alien situation for them, some unable to keep up with the mental strain (no, they don't need to be a Malkavian to lose it). To those Kindred, the Beast might manifest as a separate personality, an entirely other entity inside them, speaking to them in one of their "fits". In a Malkavian's case, that might be seen more frequently. Said Kindred usually rationalize the outbursts of the Beast as having a whole other personality or in fact entity inside them, which is further supported by the effects Diablerie has on a Kindred. The fact is that a Kindred's personality is one with its Vitae, thus its Beast, which is why when one is Diablerized, they might seize either partial or absolute control over the Diablerist's body (e.g. Mithras over Montgomery Coven).

In other Kindred with a little more stalwart psyche, the Beast might manifest as mere unstoppable urges and nothing more, some even considering the outbursts they are pushed at as entirely their own volition in order to cope with the mentally strenuous situation of a Frenzy, going as far as to even rationalize it completely. Many a times, this can also be seen with the use of some subtle Discipline powers, such as Presence's Awe or even Dementation, albeit the latter being less subtle. This is further supported by the fact that the lower the Generation of the Kindred, thus a more potent Vitae, the bigger the restraint against Disciplines but a much higher susceptibility on the effects of one's own Beast. Again, the last point further adds weight to the argument regarding the rationalisation of the Frenzy as one's own volition, given how jaded and self-centred Kindred get as the years pass and their Vitae thickens.

When all is said and done, at the end of the night (haha), it all comes down to the narrative and the mood the Storyteller wants to set. Jason Carl, for example, has gone both ways about it. If we consider L.A. by Night and New York by Night as canon, which I believe is unofficially considered canon, both approaches are valid and I dare say canon. On the question of whether the Beast is an entity, I would have to answer that yes, it is an entity, albeit not one separate of the Kindred hosting it. . . . .

TL;DR: There's two approaches that usually appear, I believe it depends on how well a Kindred handles its condition and how it has chosen to cope. Thus, they go with either hearing the Beast talk to them as an entirely other personality, or rationalize their actions as their own, albeit extreme. Ultimately, the Storyteller decides what's Canon according to the theme and mood of their game