Sorry for the delay.. XMas :-)
I have found the error, and it's my own :-)
I had played around with fields, and did not use "firstname" [FIRSTNAME] in the fieldset for the event. By placing the field in the event, it was still empty, but when I manually added the name, based un the name for the registered user entering the event, it is visible.
I hoped to figure out which field in the DB that is in use, because I could then run an SQL query and update the column, but I don't figure out where to place the name.. Any hint or do I need to manually update the registration records for the events involved?