You can't. However, by default Cargo uses a different folder for cross-compilation: target/x86_64-unknown-linux-musl/release, so you still have two executables. You'll need a post-build step to copy and rename them.
I know target dirs are different, and renaming is already what I do. But I'm compiling for both native and musl targets, so the ability to have 2 different names would have been convenient.