Hi Patrick,
As you may have discovered, this form will default some settings based on how it was last used. So the first time a user tries to search on Name, then changes the filter to "contains", the next time they use the form, it should default to contains.
So, what you could do would be to perform this process with your user, then push your personalization settings to the other users of the system.
However, if the user chooses to change that filter at a later date, that change will persist for them.
Not entirely sure if there's a way to "hardcode" this default without causing some challenges with how personalizations are maintained in the system. I would coach users to check the field when they search rather than trying to code a solution.