Script to rename layer from text in the layer.

Hi, you can try the following script

var _layers = app.activeDocument.layers;
for (var l = 0; l < _layers.length; l++) {
    var _textItem = _layers[l].groupItems[0].textFrames[0];
    if (_textItem.name != '') {
        _layers[l].name = _textItem.name;
    }
    else {
        _layers[l].name = _textItem.contents;
    }
}

The above script will work assuming your layer structure is same for all. That means, Each layer will have one group and that group will atleast single textframe. If there are multiple textframes inside teh group, it will pickup the first one and use its name if exists.