Is informing a friend about reading a specific part of the Quran—while only reading Surah Ya-Sin out of shyness—considered hypocrisy, and if not, what is it called, and how does one repent from it?

What you told your friend is not hypocrisy (riya') or a lie. Rather, it falls under the category of dissimulation (tawriya) to cover yourself and to avoid disclosing your shortcomings in reciting the Quran. Dissimulation is permissible for a preponderant benefit, so you are not required to repent.