if current_name in mens_name or mens_name.upper():
    print 'I know that name.'
How would I verify the name, regardless of capitals?
if current_name in mens_name or mens_name.upper():
    print 'I know that name.'
How would I verify the name, regardless of capitals?
 
    
     
    
    Lowercase or uppercase both strings:
if current_name.lower() in mens_name.lower()
    print 'I know that name.'
No need for or here.
If mens_name is a list, you'll have to transform each element of the list; best to use any() to test for matches and bail out early:
current_name_lower = current_name.lower()
if any(current_name_lower == name.lower() for name in mens_name):
    print 'I know that name.'
 
    
    Making all words in capital case so it will be:
mens_name_upper = [name.upper() for name in mens_name]
if current_name.upper() in mens_name_upper:
   print 'I know that name.'
 
    
    Maybe this is not the best but will also works for you.
if isinstance(mens_name, list):
    names_upper = map(str.upper, mens_name)
else:
    names_upper = mens_name.upper()
if current_name.upper() in names_upper:
    #do the work here
