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Hovering your mouse over an image will bring up some of its metadata such as filename, capture date and image dimensions.
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So, here are the steps to fix this inconvenience.
When in Grid View (G) press CTRL and J together to bring up the Library View Options panel.
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Click to enable Top Label and make sure the box is set to Copy Name or File Base Name.
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That's it, in Grid View the image's file name will now be displayed above the image making it easy to copy multiple filenames without having to hover over it.
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