If you’re talking about data broker sites, in my experience, you can enter just your first and last name and look at the results to see if any of them match you. Odds are they’ll have entries for multiple people with the same first and last name as you, so your first and last name won’t be very significant information. Usually they’ll have something like a phone number shown as well, so you can see if it matches you.
Also, you can search websites like haveibeenpwned.com or databreach.com. They’ll let you enter single bits of data, like just your phone number, or a single email address, to see whether it’s been part of a data breach. I recommend not entering your full name, since that will bring up the data breaches for everyone with your first and last name, which isn’t helpful.
I’d like to add that just because your data doesn’t show anything when entered doesn’t mean it hasn’t been breached. I recently had a case where one of those sites mentioned a breach I had but not the other, which means they can miss things or take a while to add them to their database.