If you mean that Safari is not your default browser, see the following from Make Safari your default web browser on Mac - Apple Support
Safari is the default browser when you first set up your Mac. If you accidentally change your default browser or just want to change it back to Safari, you can easily adjust your default.
- On your Mac, choose Apple menu
> System Settings, then click Desktop & Dock
in the sidebar. (You may need to scroll down.) - Click the pop-up menu next to “Default web browser” on the right, then choose Safari.
Some apps open webpages in a browser other than your default browser.
Also note that Safari and Google Chrome are internet browsers, not search engines.
Search engines available in my Safari at Safari menu > Settings > Search (at top of Safari Settings window) are Google, Yhooo, Bing, DuckDuckGo and Ecosia.
Is it the browser or the search engine that is the issue?
If it is the browser, when you say " if I am using safari, it just switches over to google chrome." can you provide more details such as does it actually change while you are actively using Safari or when you click a link somewhere, etc.