The grammatical name for the phrase 'one of these houses right opposite my home' is an indefinite pronoun.
The grammatical name for the phrase 'one of these houses right opposite my home' is an indefinite pronoun.
Specifically, it is an indefinite pronoun phrase functioning as the subject of the sentence.
Indefinite pronouns refer to non-specific people or things. In this case, 'one' is the indefinite pronoun and 'of these houses right opposite my home' is the prepositional phrase modifying 'one'.