I don't know Rust very well at all, but I believe that Rust would only prohibit that if p and updated were referencing the same thing. If updated was a modified copy of p then I don't think Rust would help. But I could easily be wrong on that.
What would help is splitting the function up so that you don't have multiple named variables representing multiple versions of the same thing in the same scope:
Person doSomethingAndDots() {
Person p = doSomething(...)
...
return p
}
main() {
doSomethingElse(doSomethingAndDots())
}