If this is a one-off, does that matter?
If this is something you need to change often (green today, nothing tomorrow, red the day after) consider making that first search one that applies a character Style, eg "BirdName". Once you've "tagged" all the names with that style you just need to edit the style definition for a global format change.
Note that you can't apply an actual "Text Highlight" using a Style. What you do is apply shading in the "Borders and Shading" format options. That is in many ways better because you can also change the text colour so it pops.