We'd like to map the owner upon assignment to a custom field. For example, when a new lead is created, the routing rules are requested, and Sally Jones is assigned the owner of the new record, we'd like Sally Jones to be the value populated on another field called "Marketo Owner" so that it lives in two places. Is this possible? I have a ticket opened with support, but I'm being asked for the field names of current mapping. Is the change owner activity an actual lead/contact field if it's not a change data value activity?

I don't think you should use the word "mapping": that will just confuse Support.If you want to copy the true owner field to a secondary flat field on the person, use Change Data Value in a trigger SC. While the owner is itself not a flat field (it's more of a join) you shouldn't have any trouble copying it.