It is customary to use plural verbs/pronouns while talking about the elderly, as a token of respect. However, वह मेरा नाना है। is not grammatically wrong.
Yes. हैं is the plural form. But we often treat words that refer to people elder than us or who command our respect (like पिता, दादा, दादी, गुरूजी etc) as if they were plural nouns. So, this sentence is 'वे मेरे नाना हैं' instead of 'वह मेरा नाना है' .