In a file each record is in part a name and an event associated with that name. If a person is in 2 events, then there are two records, one for each event that person is in.

Is there a way to automatically display in a different field ("other event"), the other event? A field based on a name matching relationship puts the event from the first occurance of the person in the "other event" field of both records.

Create a self-relationship -- relate the file to itself via, say, the name field. Then create a portal with the Event field in it. That will list all the events the person is in -- in each record for that person.