Depending on the position, it might be more natural to say "[position] internship". And depending on the situation, "at [name of company]" may be redundant; if you're sending the cover letter to the company, rather than a recruiter, they probably already know what the name of their company is. More useful would be your name and the fact that it's a cover letter; if it's an email address specifically set up to receive applications for this position, then sending an email with a subject line consisting of nothing but the fact that it's an application for that position tells them nothing at all other than you have the right email address. Also, in emails, "re" is short for "reply", not "regarding", so if this is the first email, rather than a reply, you should drop that.
So something like "GrazioL cover letter for [position] internship application".