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I am fairly confident that I know the answer, but I tend to be wrong more often than not whenver I feel confident, so it doesn't hurt to ask! Which sentence below would be the correct one? I believe that it would be "whom" because my middle name is the subject. Is that correct?

"The middle name given to me at the time of my birth pays tribute both to a grandfather I have never known and to a grandfather who/whom has never wished to know me."
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Use "who." It's the subject of the clause, "who has never wished to know me."

Similarly, you would say, "He has never wished to know me," not "Him has never wished to know me."
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It's a great opening line. It would make want me read more.
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See? It's a good thing that I asked! Thank you!
If I were to write the sentence differently, would this sentence be correct:

"The middle name given to me at the time of my birth pays tribute both to a grandfather whom I have never known and to a grandfather who has never wished to know me."

Would the first "whom" be correct, being that "I have never known him" ?
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Absolutely so.

I started to add that to the original, but you were so quick you cut off my edit.
 BarbaraPA's reply was promoted to an answer.

Because you have a "to" before the clause leading directly to who/whom, I think using "whom" is correct. But had you written, "pays tribute to a grandfather, who I have never known," then that may have been correct as well.

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