Go into "Manage Database" and select your table. Then select a field. You can a) use the Validation tab to require input or b) write a script and attach it with ScriptTriggers (If you have FM 10 adv).... Hope this helps.
Another lightweight method is to use Conditional Formatting on the phone and email fields. If the name has a value, then their background is red until one of them is not empty. It doesn't really force people to enter something, but it makes it pretty obvious it needs to be done.
It also helps to have an Accounts system in place, with "modified by" fields, with a timestamp and the Account name (last auto-enter option). If you have a checkbox which evaluates true (1) for those which were not done correctly, you could Find records which were not completed, and who last modified them. Get out the ruler and whack a few knuckles :-! In other words, train people to enter data correctly, and make them aware that they will be caught if they don't.
Move on to more intensive methods if the above is too lightweight for you. But I have found that validating to enforce "not empty" is not always as easy as it sounds.