It can be done; this won't show a label on hover, but will put the text in the plot itself. (Tested in LibreOffice 126.96.36.199 but likely to work in later versions.)
Select the columns that contain the data you want to plot (but not the labels) and create a chart (Chart button or Insert->Chart...).
Choose the XY (Scatter) chart type and click Next. Then have the "First row as label" checked or unchecked as appropriate and click Next.
Once you are on the dialog for selecting Data Series and Data Ranges, select any of the Data Ranges, then define a range for the "Data Labels" (the text you want next to each point) by entering it or using the tool that allows you to select it from the spreadsheet.
Once you've clicked "Finish", either
1) Select the points, right click and click "Insert Data Labels", then right click again and click "Format Data Labels; or
2) Click Insert->Data Labels...
Make "Show category" checked. Make "Show value as number" unchecked. Click OK. You should now see the data labels. Depending on how close your points are etc., they might overlap each other; the Format Data Labels dialog box has options for font, label placement and rotation which could be useful.
If this answer wasn't satisfactory, this might help (it's more or less what I said, but worded differently): https://ask.libreoffice.org/en/question/23756/calc-insert-text-next-to-the-charts-data-points/?answer=25142#post-id-25142