This is not a topic I know very well, but I think it could be font-related.
For Instrument Names, you can add a shift baseline in the editing window, which allows you to adjust the vertical position.
But AFAIK for Player Names, unfortunately, this option isn’t available, neither in the editing window nor in the Paragraph Styles.
You should maybe start another thread with this question, and some users will be able to help you.
Or you can also have a look at these ones: