Ideally, you would like names to be volunteered as part of your conversation. However, if they are not, you must request them in order to continue your search. Request names of other contacts who might be willing to provide further advice and information, as well as referrals to search firms. Assure the person you won't be asking these people for a job. Especially ask for referrals in the functional areas you're interested in and other fields your skills and experience might fit.
Most executives are continually on the lookout for talent to help their organization.
Be aware that networking interviews sometimes transform into job interviews if your background and style fits. You can help the process, especially if you're sensitive to the possibility.