@txnelson's solution changes the text of the button, which is what the title of your post says you wanted.
But, the picture you provided looks like you want the name of the file below the button – not in the button.
If that's what you really want here's a modification of Jim's code that will get you there.
Names Default To Here( 1 );
New Window( "Data and Limits file",
<<modal,
Spacer Box( size( 10, 10 ) ),
Text Box( "Choose a data file:" ),
BB1 = Button Box( "Pick file",
D = Pick File();
If( D != "",
file1 << set text( D )
);
),
file1 = Text Box( ),
//Text box(L),
Spacer Box( size( 20, 10 ) );,
Text Box( "Choose a limits file:" ),
BB2 = Button Box( "Pick File",
L = Pick File();
If( L != "",
file2 << set text( L )
);
),
file2 = Text Box( ),
//Text box(D),
Spacer Box( size( 20, 10 ) )
;
);
-Jeff