This has nothing to do with embarrassment, and everything to do with credibility. Not advertising where you submitted your paper is part of a much more general principle that I recommend to everyone to follow. Here it is:
NEVER brag about an achievement that you have not yet accomplished.
The reach of this principle extends far beyond academia, but academia is one place where it is particularly important, since research communities are small and very soon after you enter one, everyone in it will know exactly who you are and what you are about. It is therefore crucial to establish your credibility from day one.
Imagine two researchers, Alice and Bob. They work in the same field and are equally talented, but:
Alice waits until her paper is accepted before listing the journal on her publication list, and Bob doesn't.
Alice does not list "in preparation" papers on her publication list. Bob always has several of them listed.
Alice only gives a talk about her latest results after she has finished writing the manuscript and checking all the details, and has either posted the paper online or is getting ready to do so very soon. Bob gives talks about unwritten projects that are very far from fruition.
Alice's papers are very careful to claim only the results that she has rigorously established, and not rely on future as-yet-unwritten results. Bob's papers often make rosy promises about future extensions of the work he has done and how important they are, or will be.
Here's what will happen. Initially, Bob will be able to attract more attention than Alice from senior researchers in the field. At the early career stage when researchers like them are still judged by fairly superficial metrics, his publication list will appear longer, with catchy journal names his papers are "submitted" to. His talks will be more exciting, with mention of great results that he is working on and is confident he'll have written soon. But then... pretty soon people will find out that he is full of hot air. Many of his projects will not materialize. Many of his papers will be rejected from the fancy journals and quietly published in second-rate journals. Sure, he will have some successes, just like Alice, but after a while he will find that when he goes to a conference, much fewer people come to listen to his talk than to Alice's talk the same day. He will notice that when she announces an exciting result she has been working on for a long time, she has a paper to back it up, and people are much more impressed by that than when he announces a similarly exciting result. And he will notice that when he submits a paper, the referee report always comes back with many complaints about the unfounded claims he makes in his papers, sometimes citing them as the reason for rejecting the paper or requiring a major revision.
Even when he does finish a nice paper, Bob will notice that since he already gave a bunch of talks about the result, the community has moved on and the result is no longer seen as very exciting, again reducing the impact of his work just when he is about to submit the paper and needs that excitement to be at its peak.
After a few years, Bob will notice that despite him and Alice being about equally talented researchers and publishing a similar output of good papers, Alice is more successful than him. Her papers are accepted more frequently, to better journals, and she is more respected and appreciated by her community. That is the point when he understands the principle I mentioned above, and starts to follow it himself.