In database 1, create a script that uses Perform Script to perform a script in database 2. Pass the values of these two fields as a script parameter to that script in database 2.
Your expression in the optional script parameter box can be: List ( YourTable::LastNameField ; YourTable::FirstNameField )
Then your find script can be:
Go to Layout [specify layout on which you want to perform your find here]
Enter find Mode  --> clear the pause check box
Set Field [YourTable::LastNameField ; GetValue ( Get ( ScriptParameter ) ; 1 ) ]
Set Field [YourTable::FirstNameField ; GetValue ( Get ( ScriptParameter ) ; 2 ) ]
Set ErrorCapture ( on )
Note that this method assumes that FirstNameField in database 1 will never be blank. A different approach to passing multiple values in a single parameter must be used if both fields might at different times be empty.
Is it possible to write this out more in detail for me. I don't quite know what to do in which database when i'm reading your answer. Where should i use the optional script parameter? How to do so?
In database 1, you have a single line in a script or attached to a button:
Perform Script [ "Script Name in Database 2 goes here" from file: "database 2" ; Parameter: List ( YourTable::LastNameField ; YourTable::FirstNameField ) ]
The script in database 2 that this script step in Database 1 performs is the script that I posted previously.
An alternative approach is to add a table occurrence with an external data source reference to Database 2 inside database 1. Then you can set up a layout to this table from Database 2 in Database 1...