so, i'm pretty sure you're here from this post, or at least have seen it, but for anyone who hasn't, here's the basic gist of dream's aspects work so i'm not rehashing that all here
and to your actual question! the short answer is no, i don't believe dream has a preferred form, though he probably has aspects of presentation he prefers, and that's why all versions of dream tend to be black and white and on fire
(and yes, the reason we mostly see that one is bc that's the one the audience by default sees)
the long answer does have major comic spoilers, that's unavoidable for the stuff i need to explain, so here's your heads up on that since i'm not sure how caught up you are
but to dig into all that! first off, the reader/audience is definitely a character in the story, and the endless are aware of this. it's a story most likely narrated by dream, for the most part, and then just hijacked by other narrators when they need to get their point across
this is something that stayed in the show too actually, and i do love that we get dream's narration at the start of episode one, because the reason we're seeing this is he is a storyteller by nature and he has invited us to see this! but throughout the comics too, especially in the early issues, dream's inner narration is a narration, he's not just talking to himself, he's talking to us
this is explicitly confirmed at dream's funeral, because we are one of the dreamers invited to watch - and the last one to wake up
and my other favourite instance proving this? the end of brief lives. where desire grabs the narration and forcibly turns it away.
up until now, they've had no problems with us watching, they like the attention, and performing all this for an audience. but here? where it's extremely implied that they're worried about dream and that this might have been their fault? no. desire doesn't want to share that. we're nosing too deep into their business now, and whatever it is they're thinking in this moment, it's private
(and there's our proof too that it's all endless who can do this, not just the storyteller, because we see a lot of mortals' private inner thoughts leading up to this, and it's only when we get to desire that the narration tells us to fuck off)
so, since the reader is a character, and presumably a human one, we're gonna see a human dream, and the one matching the modern english speaking western world, until the comic or the show deliberately switches perspective and then we see that one
which could just be the final answer to your question and i could end this here, but i think there's actually an additional supplementary answer here
which i think borders on headcanon? certainly people have disagreed with me on this before, but it's the way that makes sense to me in terms of what we're given in the story
so like. the endless are more than three dimensional beings. we don't know how many dimensions, but enough that a three dimensional being can't ever see their entire shape at once, hence why they look different from different perspectives despite not ever changing
and that's an easy answer not too difficult to understand. but then things like overture come up, where we see multiple facets interacting. and it's a bit more complicated than just these are all the sides to the shape that is dream. we've got both the overarching dream, the whole being, every facet at once, and we've got the individual facets that all move in slightly different ways
it makes me think of like... you know if you've ever seen a dance performance, where many performers are acting as different parts of a whole creature? and they all move slightly differently, but it's through that you see the movement of the singular creature?
every facet of dream is moving through slightly different versions of dream's life. and dream's life isn't any one of them, it's all of them at once, but if you wanted to, you could still focus on one of those performers
which i think the story does
because in overture, in the meeting between all of dream's facets, our dream arrives late. because he was held up dealing with the corinthian. so all of the other facets must have either dealt with the corinthian faster, in their version of canon, or chosen to prioritise this meeting.
they're moving differently.
but still, as the meeting between the facets continues, now that they're all in one place and synchronized again, they start to fold back into one being. say all the performers are standing in a line, and now you can't see every individual one, just the creature. and the existence of the endless continues like that, moments of synchronization and moments of ever so slight disparity weaving in and out of each other, because if dream's facets are all based on the culture perceiving them, they physically can't be doing exactly the same things all at the same time, reality has to distort just a little bit around them. (and we know they do distort reality with their presence, it's something del likes to talk about, and in extreme cases we get things like the reality storm)
it's why desire's trick in overture works, because the human facet of dream can believe that the cat facet of dream is just deciding not to synchronize with the group bc cats. and cat desire only ever talks about parts of dream's life that they know about (dream's love life, how shitty their parents are), so dream doesn't realise that's not him
(side note i do love this scene bc desire doesn't know what happened to alianora. they're asking bc they cared a lot about alianora and was genuinely hoping this would end well)
but i think that's the other reason we see one specific aspect of dream so much. because the big moments in dream's life, those are consistent across facets, but the minor details? those can shift. so if we wanna see those minor details, we have to pick one performer to focus on
and in this case, that's the morpheus we're used to