While your name dies out,the daughter continues the lifeline of another man in another family.
What grammatical name is given to this expression ' the lifeline of another man' and what is it function?
Normal word order in English sentences is this:
subject / verb / object or complement
http://www.chompchomp.com/terms.htm
Look those terms up here and then let us know what you think. Hint: ignore the dependent clause ("While your name dies out")
Personafication
The expression "the lifeline of another man" is a noun phrase. Noun phrases act as the subject, object, or complement in a sentence. In this case, it is functioning as the object of the verb "continues" in the sentence.
To identify the grammatical function, we can break down the sentence:
Subject: "the daughter"
Verb: "continues"
Object: "the lifeline of another man"
In this sentence, "the lifeline of another man" serves as the direct object because it receives the action of the verb "continues." It is the thing that the daughter is continuing.