If Dauntless Bodyguard enters the battlefield at the same time as another creature, that creature can’t be chosen for its ability.

If the chosen creature leaves the battlefield, you can’t choose a new creature for Dauntless Bodyguard to protect. If you activate its last ability in this case, no creature gains indestructible.

Dauntless Bodyguard’s first ability isn’t a triggered ability and doesn’t use the stack. Players can’t respond to your choice of which creature it’s protecting.