That’s what makes Tony Tony

In each below, should there be an intervening comma between the two repeated words?

That’s what makes Tony Tony. (what makes Tony who he is.) That’s what makes her her. (Same logic.) That’s what makes him him. (Same logic.)

Thanks.

If these two last words at the end of the sentence were different, you wouldn't put a comma in:

That's what makes a house a home.

So you shouldn't put a comma in even if they're identical.

Should there be an intervening comma? Yes.

That’s what makes Tony, Tony.

The Chicago Manual of Style (13th ed) says:

For ease of reading, it is sometimes desirable to separate two identical or closely similar words with a comma, even though the sense or grammatical construction does not require such separation: "Let us march in, in twos." "Whatever is, is good." But: "He gave his life that that cause might prevail." (Source: CMOS, Paragraph 5.56)

Note that the "sense or grammatical construction does not require such separation"; however, the comma provides a small indicator to the reader that there should be a short break (and possibly intonation change) after the first "Tony."

Either is acceptable in published writing.

I tested this with an analogous set of examples to your own:

(1) That's what makes you you

(2) That's what makes you, you

Among the books conforming to (1) are Thankless in Death by J.D. Robb, But Don't Call Me White by Silvia Bettez, and The Paris Affair by Teresa Grant.

Meanwhile, the books conforming to (2) include Vows by John Porec and The Diary of Margaret Evans by Alyanna Tate.

So in practice the usage is up to the editor and writer.

The Chicago Manual of Style (17th edition; may be paywalled) also allows for both. Paragraph 6.55 leaves the clarification up to the editor:

For ease of reading and subject to editorial discretion, two words that are spelled alike but have different functions may be separated by a comma if such clarification seems desirable.

Let us march in, in twos.

Whatever is, is good.

but

“It depends on what means means.”

Their use of italics suggests an emphatic alternative: