No matter where I am, you'll always be mine
Mia is "mine" in Spanish.
An association of a sport makes me a food to dine
She co-hosted some talks for NBA, giving her "food to dine".
I died in film in the 2000s not to early
In 2017, Mia Sutton dies in "Death Note" film. Probably, hundreds of Mia died in films. I just chose one. Also, this might refer to the threats she received for "performing" with a hijab.
America murders me when I channel the otherworldly
There were rumours about her death in a car accident. She also received many threats for "performing" with a hijab.
Speaking of that, I am a pet of many names
Mia Callista and Mia Khalifia are some of her "other names". "Pet" might refer to her "adult industry job" and the names she'd been called.
A Dubai tower and rapper made my body sold, it claims
Burj Khalifa Tower in Dubai and Wiz Khalifa (rapper).
I feel dirty for answering this, but I'm convinced this one is the answer.
Particularly, the first and the last line gave it away.