When you're not a technical person, anything online can be daunting.
Confusing enough that you want to step back and hand control to someone else.
Don't do it.
Hiring an expert to perform a task you're not equipped to do is sensible. Allowing them to be the only ones who have the keys to your premises isn't.
And, that's what the login details for your website's domain and your website itself are... they're the keys to your front door.
Your web designer needs to have access to your website, or they can't develop or maintain it. But, they're your keys and you need to be the one handing them out. Have you got 'em safe?
It's an online world and your website is a vital part of your business' survivial. If something happens that your web designer can't help you any longer, you need to be sure the show can go on.
If you've lost access, there's a way back. Expect that it might involve proof of identity - forms, driver licenses, birth certificates - depending on the provider you're dealing with.
That might be frustrating but take comfort in the fact your site is still your site.