No, there isn't an easy way: for our project, we did this by hand. We've filed a ticket for this: #203297 ("Use different captions for search buttons: show filter vs filter"). Currently, it's not scheduled for a release within three months.
Don't you just mean the Caption of the button? That should be editable from your data-grid by default, right?
Same problem here. As a workaround we use the default value and every deployment to acceptance we first change this value using the 'Batch translate' option.
Perhaps I miss something, but in my case I even didn't want a label on that button at all. We use icons (like a magnifying-glass for a search-button).
So in the css-file I added a background image for the search-button, and I changed the System text 'Data grid , Search' in an empty value. That is, I needed to leave a not empty string in the field (ASCII 32)!
I expect that you can just add every value you like in that system text.