Why you’re getting stuck at >

The leading $ in your example is the problem. In your shell session, the $ is just your prompt marker (not something you should type). But when you copy-paste with the $ included, Bash interprets it as part of the command, and it becomes:

$for name in "${theList[@]}";do echo $name;done;

Correct usage

Just drop the $ when running commands inside your shell. Example:

declare -a theList=("joey" "suzy" "bobby")

for name in "${theList[@]}"; do
    echo "$name"
done

Output:

joey
suzy
bobby