create a matrix/database from intersection of multiple files

I have a file with a list of names, and several files which contain each some of those names. i want to create a database with the list of names as the first column, the list of files as the first row, and place zeros and ones for if the name exists in the file or not. example:

names.txt:

APHSKNCTA      
YPPASTTKI 
HPSFARFAL 

file.txt:

1 theName      APHSKNCTA 
1 theName      YPPASTTKI  

file2.txt:

1 theName      APHSKNCTA  
1 theName      HPSFARFAL 

expected output:

            file.txt     file2.txt    
APHSKNCTA      1            1
YPPASTTKI      1            0
HPSFARFAL      0            1

my code so far is here below, and it gives me the intersection of each file with the list of names, but now I don't know how to, from this, print the 0s and 1s at the place I want.

directory = r'/home/Run'
for entry in os.scandir(directory):
    thefiles = set(open(entry).read().split())
    namess = set(open("names.txt").read().split())
    inter = thefiles.intersection(namess)
    print(entry)
    print(inter)   

output:

<DirEntry 'file.txt'>
{'APHSKNCTA, YPPASTTKI'} 
<DirEntry 'file2.txt'>
{'APHSKNCTA, HPSFARFAL'} 

I suppose I have to do an if statement, but is not as " if thefiles.intersection(sbpeps) = TRUE " worked that way. does any one have an idea or just some direction to point me to? i'm lost and stuck on this for not knowing what to search for. thank you!