Why not use the -c option? Especially if you're using Bash or Zsh which has "here-strings":

    checksum() {
      hash="$1"
      file="$2"
      sha256sum -c <<< "${hash}  ${file}"
    }

Or if you need to use a POSIX-ish shell:

    checksum() {
      hash="$1"
      file="$2"
      printf '%s  %s' "$hash" "$file" | sha256sum -c
    }

Of course you can add a `--binary` option (uses '%s *%s' instead of '%s %s'), options to use different hash functions, etc.

I also think it's weird to use `alias` inside a function, instead of just using a parameter to store the name of the program to execute.