I routinely break up what one person is saying or thinking into more than one paragraph. I do it for emphasis and to keep the paragraphs short. The second paragraph is a different idea, or a change in focus, or whatever. Who is speaking has to be obvious. One can omit a final close quote mark to indicate continuation, but lots of readers are ignorant of that convention. Often I add some bit of physical description between the paragraphs instead. That kills two birds with one stone because who is speaking is clear and the scene isn't just talking heads.
I mostly write--or try to write--in deep POV. The description must clearly be from that person's POV, so then there's no dialogue tag needed in the first paragraph and none in the second, either. If it looks as if the second paragraph might cause confusion, I add a dialogue tag.
I also try not to let my characters be long-winded, but I do write dialogue-heavy books. I make a point of keeping the conversation batting back and forth. I used to hate reading books in which someone would ask a question and the other person would not answer them. That's real life, and it suits a mystery, perhaps, but it doesn't suit a romance. In a romance, one should always get the feeling that these people can interact with each other on a comfort level they don't necessarily have with others. My opinion, anyway; I don't like to write stories about people who can't talk to each other and will get divorced in a year.
