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Tommy (playing the piano): Are you feeling that?
Jude: Yeah, it's okay.
Tommy: Okay? When this song hits, Becomes famous?

Shay's going to wish he had a last name to change. Change his name so no one
would recognize him?

Let's get to the lyrics.
Jude: Are you seriously going to sit there right now
and pretend this is only about Shay?
Tommy: Jude, don't start.
Jude: I didn't, you did, remember? You kissed me?
Tommy: You wanna keep your voice down?
That's not what we talked about.
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MadhulkTommy: Okay? When this song hits, Becomes famous?

Yes, when it makes an impact.
Madhulk
Shay's going to wish he had a last name to change. Change his name so no one

would recognize him?

I'm not sure. Without knowing the full story I don't think it's possible to say. If your explanation fits the plot then it could be right. If there is no obvious allusion to anything else in the story, and the character Shay would share in the song's success, then it may just be a reference to the fact that famous people in showbiz often adopt a stage name, and this may just involve a change of surname (e.g. David Jones called himself David Bowie).
Comments  
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The plot is that Jude and Shay had a relationship that didn't last very
long. So to get even with Shay, Jude has to write a song that's supposed to
make Shay feel bad for dumping her.
Madhulk
The plot is that Jude and Shay had a relationship that didn't last very

long. So to get even with Shay, Jude has to write a song that's supposed to

make Shay feel bad for dumping her.


In that case your interpretation seems reasonable.
Thanks, Mr Wordy!
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