If a cover letter is needed at all, its purpose nowadays is usually to include information for which there is no appropriate form in the journal’s submission system (which can inlude suggested reviewers, unwanted reviewers, informations about prior submissions, etc.) – see also these two questions.

I do not see how the information that you are a PhD student is relevant to the editor or anybody involved with the paper, so I wouldn’t mention it. Every spurious information in that letter just wastes the editor’s time. I submitted a few papers as a PhD student (with and without coauthors) without mentioning this fact and did not encounter any problems that I would even remotely relate to this.

If a cover letter is needed at all, its purpose nowadays is usually to include information for which there is no appropriate form in the journal’s submission system (which can inlude suggested reviewers, unwanted reviewers, informations about prior submissions, etc.) – see also these two questions.

I do not see how the information that you are a PhD student is relevant to the editor or anybody involved with the paper, so I wouldn’t mention it. Every spurious information in that letter just wastes the editor’s time. I submitted a few papers as a PhD student (with and without coauthors) without mentioning this fact and did not encounter any problems that I would even remotely relate to this.