How to dynamically add wordpress shortcodes

Assuming the $row->internalFunction is a function, or the name of a function which already exists, then you can do something like so:

foreach ( $dbQuery as $row ) {
    add_shortcode( $row->formName, $row->internalFunction );
}

So if the formName (shortcode tag) is foo and internalFunction is foo_func, then [foo] will be handled by the foo_func() function:

// The standard/non-dynamic way.
function foo_func( $atts = array() ) {
    return 'something good..';
}
add_shortcode( 'foo', 'foo_func' );

See the Codex for further details/guide.

Or here’s an example of using closure:

foreach ( $dbQuery as $row ) {
    $func = $row->internalFunction;
    add_shortcode( $row->formName, function ( $atts = array() ) use ( $func ){
        return $func( $atts );
    } );
}

Or did I misunderstand your concept?

UPDATE

is there a way I can pass parameters into the internal function

Yes, you can pass custom parameters to the internal function (internalFunction); but you’ll do it via the closure:

foreach ( $dbQuery as $row ) {
    $func = $row->internalFunction;
    $params = json_decode( $row->json )->params;
    add_shortcode( $row->formName, function ( $atts = array() ) use ( $func, $params ){
        return $func( $params );
    } );
}

Basically, use the use keyword to make variables in the foreach scope be available in the closure.

And you could even pass the entire $row object..

foreach ( $dbQuery as $row ) {
    add_shortcode( $row->formName, function ( $atts = array() ) use ( $row ){
        $func = $row->internalFunction;
        // Here you can pass $row->formName to the function.
        return $func( json_decode( $row->json )->params );
    } );
}