Indy does it, but Ava doesn't.
But, with Indy, it's a learned response. Before we got Ava, he'd run to greet people without a toy. When Ava arrived, all that changed.
Ava is much more insistent that she get the attention when someone arrives. She'll force herself between the guest and Indy. So, Indy resorted to running into the TV room and grabbing a toy as an offering to our guests.
He has refined the tactic to the point that when they see someone arriving, Ava will run to the door to greet them. Indy will select a toy, then wait at the door beside Ava.
When they come in, Ava will "sound off" to get attention, while Indy will stand in front of them, with his gift.
This began when Ava was a small puppy, and as we know, people seem to love puppies more than grown dogs. Well, maybe they don't love them more, but puppies seem to get more of our attention than older dogs.
It's the same as it is with babies. People love to fuss and coo over babies, but don't demonstrate the same interest once they get past the toddler stage.
Anyway, Indy soon figured this out, and after the first few people just had to hold, or show attention to the little white girl, he resorted to bringing an offering to our guests.
It works, because it usually provokes a chuckle or laugh, and they can't resist that pleading face, as he proffers his friendship in the form of some well gnawed toy.
Make no mistake, Indy is definitely the alpha. But, he is secure enough in his position that he will defer to her except in instances when it really matters, such as a squirrel that needs to be driven from their yard, or when something else needs to be barked at through the window. If she doesn't get behind him on her own, he'll put her in her place.
He is quite the gentleman however, he does it with attitude and an aggressiveness that stops short of violence, and she does get the message.
Tom