I have a slideable right panel, which has two tabs: search and filter. These two tabs have form fields which allow users to refine their search result displayed in the main section. The options I came up with are the following: Refine Panel and Refine Results. I also want to reuse the name of this panel for places where users can find tools and filters in the application.
"Refine" is used quite commonly for this. If you have enough space then "Search & Filter" may be a better option since it exactly describes what's hidden behind the button.
First of all, a bit more clarity in your use case might be helpful. But if I understand correctly you want to provide search and filter in a slide in panel.
My first thought is that this might not be the best pattern to use. Most often I see Search as either an option on the main list screen, or a separate screen of its own... but not as a modal element on top of the main screen (such as a slide-in panel). Either way, the results usually show up in the main screen.
The FILTERS, however, can be presented in a slide-in panel - a fairly common pattern. In fact, I designed an app that worked just that way. The main list was shown on the main screen, searching could happen on that screen, and filters were in a hideaway panel that slid out (effectively) from the right:
Does this pattern make sense for your app?