Change Spaces to Dashes?

You could simply use str_replace:

str_replace( ' ', '-', $name )

In your code, this would translate to:

return '<img src="https://wordpress.stackexchange.com/images/flags/" . str_replace( ' ', '-', $name ) .  '.gif" alt="' . $name  .'" title="' . $name . '" class="flag tooltip" />';

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