I am a student. I silently recite the Buddha’s name while I walk to school. At home, I would also silently recite his name while doing the household chores.
At night I would then silently dedicate the merit and virtue as [the typical dedication of merit and virtue verse].
Is that correct?
Yes, this is a very good practice. Please keep it up: it will bring you peace and happiness. I would like to recommend that you also listen to Great Master Xuan Hua’s Dharma talks when you can as they are especially beneficial to your practice.