LLC on deed vs. LLC for "rental business"

Hi,

My wife and I just bought our first rental property (yes, FINALLY!) and we have the property/mortgage in both of our names. Instead of transferring ownership to the LLC we just created, can we say the LLC handles all of the "property management" side of the business?

I'm assuming if someone tries to sue us, they would sue the property management LLC, not the home owners and we would have that layer of protection.

Any thoughts/recommendations?

Thanks