Throughout the series, there are subtle hints at Ichigo's real heritage.
At least... tell me your name.
Ichigo Kurosaki: Ichigo Kurosaki.
Ikkaku Madarame: Huh, Ichigo? That's a good name.
Ichigo Kurosaki: You think so? No one's ever told me that before.
Ikkaku Madarame: Yeah they say that guys with Ichi in their names are overflowing with talent and good looks. At least that's what I've ...
Ikkaku Madarame: ...