There are some mathematicians who are active online and who blog about their work at various stages, including when they upload a paper to the arXiv. I like this aspect as it gives a chance for the author to give a more informal explanation as to how the results were arrived at or how to interpret them. However, I've seen a few times they they say, on their blog or in the arXiv comments, that the paper is submitted for publication (which is perfectly fine), but additionally specify exactly which journal it has gone to.
As these mathematicians are in fact well-respected and solid in their career I do not wish to impugn their decision, but it smacks of me of being rather confident that the journal will accept the paper, after some small revisions. Since the refereeing process in mathematics takes months, at a minimum, and up to a couple of years in more involved cases, the statement that the submission is to a particular journal will stand for a long time before we know either way as to the result.
As a early career researcher I wouldn't presume to proclaim the journal I think my work should be published in. But am I selling myself short? Let us say I am reasonably confident the paper I am submitting is a good fit for the chosen journal, should I also stake my claim during the preprint phase, to signal at least how "good" I think my paper is? (which judgement people can then assess based on their own experience)
Edit: I see the answers at the previous similar question, while acknowledging the practice to be field-dependent generally warn against this behaviour. However I am observing a career-stage-dependent behaviour in my field contrary to those good suggestions, weighted towards those who already have some advantage (to borrow from Dan Romik's example, imagine Bob could always carry through on his promise, never overstepping the bound on what had actually been done).