Specifying a preprint is "submitted", *to a specific journal*
No, do not specify the journal that you have submitted to.


Anyone can submit a bad paper to a prestigious journal. The sole fact of submitting your paper to journal XY can not be used to signal or suggest a certain quality of the paper or the author.
If your paper is rejected by journal XY you are forced to update your publication list and are in fact publicly admitting and documenting that your paper has been rejected by journal XY.