Well actually he said he had to show "berat sahin" on the displays so it should be MOD11 if there is no space when the cycle repeats, but you're right, it would make more sense to add another space at the end.I think you meant MOD12 -- I suspect you overlooked the required space between first and last name.
Yes, the logic design would be kind of hellish with my initial approach, but I wasn't sure if it was possible to create a state machine for this problem since the character 'a' is repeated as you mentioned. Anyways that is probably a much more sensible solution and I hope it helps.Another approach, which is less flexible but results in considerably fewer gates, is to have the states be the necessary encodings of the characters. If no characters where used twice, this would require one FF per display segment. Since 'a' is used twice, an additional FF can be used to indicate whether it is the first 'a' or the second. Similarly, it can be used to indicate first space or second. For his name, that eighth FF could very nicely serve as indicating first name or last name, which makes turning on the red and blue LEDs trivial.