Without knowing what 'disp' exactly is, it's difficult to answer your second question. With the 'normal' LCD, you can simply print the string
// print name on lcd
lcd.print(names[a]);
// go to next line on lcd
lcd.setCursor(n,0);
For the first question, you're not copying the terminating nul character. So the answer to your comment 'is this necessary' is yes. If you use strcpy(), you don't need the strlen(), memset() and don't need the loop.
strcpy(names[a], entryName);
Note:
not tested.