As for picking up kids, every place I take my kids to (school, camps, daycare, etc) require you to specifically list who is allowed to pick up their kid, no matter what their last name is. Even if you have the same last name, they aren’t going to hand the kid over unless you are on the list.
It would be crazy to let anyone pick up any kid with the same last name. Think about all the Garcias and Smiths and Kims in the world… they could pick up so many kids! Plus, most kidnappings are done by family members; any institution who hands over a kid just because the name is the same is going to open themselves up to so much liability.