You should. The Google Ads account, the billing, the conversion tracking and Google Analytics should all be in your business’s name, with the agency given access as a user or through its manager account. That way you keep the campaigns and years of performance data if you change agencies.
To check, sign in to Google Ads and open Admin, then Access and security. You should see your own login with admin access. If you cannot sign in at all, the account almost certainly belongs to the agency.
Agency-owned accounts make leaving expensive, because the history and learnings stay behind. Scalepoint works inside your own account and never marks up ad spend.
This is one part of a bigger picture. How to choose a Google Ads agency in Australia covers fees, ad spend, account ownership, proposals and timelines in one place.