Not sure what starter solution you refer to but obviously the data is not normalized correctly.
The contacts name in the event should be a display of the contacts name from the Contacts table via a relationship, usually via a ctcID field relationship
When the say starter.. they mean just that and you usually get what you pay for.
Check to is how the contact name within the project table is getting auto filled.
Another possibility is that it IS from the contact table but from a full name display and the full name field is not getting updated when the FN/LN fields are changed.
Check the relationships and look at the Full Name fields in both table to see what is going on
Hope this helps
It may not be a data-normalization issue. There may be an auto-enter via lookup taking place which captures the data (name) at the time the event is recorded so that it is not intended to change with later revisions. This is more common practice with things like invoicing prices, where you want the price at the time of invoicing, without any risk of the price on the invoice being affected by price changes months later.
If it is a lookup, you can simply replace the field in question on the layout(s) with the related name field so it will always be updated. (Be careful about allowing direct editing of the name field via the related record, as that will also affect all records related to the parent record.)
I looked into using the Event Management starter solution a while ago and was not overly impressed. From what I recall it did not even have a person table.