What is this part of the reel called?

[MaxxiD]

And what do I do if it comes loose?

Sh***y pic I know. It's the bit that spins around. Has the bail on it?

It's loose, but appears to be functioning

[HL_transplant]

Rotor I'm thinking

[MaxxiD]

Rotor I'm thinking

Yes! You nailed it. Thanks

https://www.google.com/search?q=spinning+reel+rotor+wobble&oq=reel+rotor+&aqs=chrome.2.69i57j0i22i30l5j0i15i22i30j0i22i30.91 93j0j4&client=ms-android-rogers-ca-revc&sourceid=chrome-mobile&ie=UTF-8

[MaxxiD]

Remove the spool and tighten down the nut that is sitting against it. Then,tell your buddy that sold it to you that it is unfixable and get your money back haha

[SamSteele]

Like MaxxID said, remove the spool and tighten down the brass nut that holds it in place. Note that it is usually reverse thread in my experience.

[MaxxiD]

Like MaxxID said, remove the spool and tighten down the brass nut that holds it in place. Note that it is usually reverse thread in my experience.

True words. It was reverse thread