The reason for the error is that the nextInt only pulls the integer, not the newline. If you add a in.nextLine() before your for loop, it will eat the empty new line and allow you to enter 3 names.
int nnames;
String names[];
System.out.print("How many names are you going to save: ");
Scanner in = new Scanner(System.in);
nnames = in.nextInt();
names = new String[nnames];
in.nextLine();
for (int i = 0; i < names.length; i++){
System.out.print("Type a name: ");
names[i] = in.nextLine();
}
or just read the line and parse the value as an Integer.
int nnames;
String names[];
System.out.print("How many names are you going to save: ");
Scanner in = new Scanner(System.in);
nnames = Integer.parseInt(in.nextLine().trim());
names = new String[nnames];
for (int i = 0; i < names.length; i++){
System.out.print("Type a name: ");
names[i] = in.nextLine();
}