There are quite a few ways to do this, and they have varying degrees of speed/set-up time.
An easy but not-really-performant solution is doing two "do a search for"s and merging them. This works decently if you don’t have a lot of data base entries, but might start slowing down if your app scales.
You could also set up a redundant field which is Name + Last name which would act as your search field. This would allow you to retrieve your desired users by doing a single search, rather than two. You have to set up workflows to create this field when a user signs up, workflows to correct this field if a user were to change names. And if your app is already live, you need to create this field for existing users.
I am sure there are other ways but this could get you headed in the right direction.