Why doesn't symbol name come in when dragging to asset export panel?

the problem is the Symbol Item's name (or lack of it), for a strange reason, the "name" you see in the Layers panel is not the Symbol Item's name, it's the actual Symbol's name. So as far as Javascript is concerned, the symbols you dragged to the artboard are NOT named. 

If you explicitly name your Symbol Items then you'll have no problem, the Assets would be named accordingly, but you're back to square one, naming your symbol items is the same as naming your assets.

try this script, select one or more symbol items in your artboard before running.

// add selected symbol items to the Assets panel and name them accordingly
// carlos canto - 07/20/2021
// https://community.adobe.com/t5/illustrator/why-doesn-t-symbol-name-come-in-when-dragging-to-asset-export-panel/td-p/12190183

function main() {
    var idoc = app.activeDocument;
    var sel = idoc.selection;
    
    var asset;
    
    for (var a=0; a<sel.length; a++) {
        asset = idoc.assets.add(sel[a]);
        if (sel[a].typename == "SymbolItem") {
            asset.assetName = sel[a].symbol.name;
        }
        else {
            if (sel[a].name != "") {
                asset.assetName = sel[a].name;
            }
        }
    }
}

main();