I notice you've got spaces around it, so the first thing I would do is trim.
personAndPhone = personAndPhone.trim();
Next, you've got a space in the middle, which might be a nice splitting point.
String[] tokens = personAndPhone.split(" ");
String name = tokens[0];
// now contains: Dave
Next, you can remove the brackets from the number:
String number = tokens[1].replaceAll("[()]", "");
// now contains: 206515608
Or as @EvgeniyDorofeev put more concisely:
String[] tokens = personAndPhone.trim().replaceAll("[()]", "").split(" ");
String name = tokens[0];
String number = tokens[1];