Kittens show they've bonded with their owners by rubbing their heads against them, being affectionate and playful, and looking to their owners for food when they're hungry. Typically, a kitten can learn to recognize its name within about two months.

Signs a Kitten Has Bonded With You
First and foremost, once a kitten has established trust with its owner, it won’t be resistant or try to run away when its owner approaches or pets it. On the contrary, it will rub its body, head, and tail against you. This physical contact is a clear sign of affection and bonding.
A kitten that sees you as its owner will also be very affectionate and playful, constantly seeking your attention. They might rub against your legs, purr, or expose their belly – which shows they trust you and feel safe. If your kitten constantly circles your feet or follows you closely when you decide to go out, it's a sure sign it has identified you as their main caregiver; it doesn't want you to leave it.
Kitten Affection and Dependency
When a kitten is content after eating, it will actively seek your company and enjoy sleeping or cuddling next to you. These are all displays of a kitten feeling safe and comfortable around you.
When a kitten is hungry, it will no longer search for its mother for food; it will instead seek out its owner. This shift in dependency indicates the kitten now views its owner as its primary caretaker.
Responding to Your Voice and Cues
After a bond is formed, kittens will become very attuned to their owner's voice. When you call them, they should come running to you and will often display physical affection. However, if there is little or no reaction, it might indicate that the bond of trust is not fully established yet. Consistent positive interactions help solidify the trust and the bond with your kitten, further strengthening your relationship. Kittens recognize those who care for them, and their actions will show it.