You missed out the deceased part out... :/
Therefor, your theory is wrong, period.
Patamon was getting worried, she's been gone for a while and he didn't like the awkward silence. It made him feel extremely lonely and he met Gatomon to destroy his depressing feelings. When he met Gatomon, she was lonely too and it made him feel happy to have something in common with someone. He knew that if he started to hang around with someone, they would both feel better and now, he was still alone, sat there waiting.
He sighed and then said:
"Ahhhh... I am just SO bored! ... Oh, maybe I can see her from a birds eye view*
He soared into the sky and he saw her, running his way. He grew happy as a cheesy grin snuck onto his face.
She WAS coming back! He knew it and for once, he was right, he felt victorious. He landed quickly before Gatomon saw him in the sky.
"Hmm... how lonely it is down here without somebody... I think I know how she feels!"
He murmured to himself.
Patamon kept on sitting, waiting, he was getting cramp in his wings and decided to lift himself off of the ground.
"Uggh... my wings... I need to stretch them."
He flew in circles around the area, not really wondering about where Gatamon was, he knew that she would return.
Who would hurt somebody as cute as Gatamon? He thought to himself as positively as possible, settling down finally.
"Hmm... I will sit down again, I have to wait for Gatamon, she is being so kind and she might think I have left her alone... I would hate to see her upset over something that I have done!"
He quickly sat down and waited for his precious Gatamon friend.
[I give them different personalities, though sometimes my own beliefs worm their way in. But generally, they are different. Why'd you ask?]
"So you're happy down there?" Maxwell asked as Shadow blabbered on about his home-life, girlfriend, the earth and what year it was down there, and everything far and near in between. It was riveting to hear about the outside world; time worked differently here, therefore placement and invention worked differently too. Some of the things Shadow had mentioned, like helicopters and televisions, he had never even heard of. They sounded fascinating!
"More than happy. Though... we miss hanging around you, and Robyn," he said, mumbling the last part so as not to make Maxwell uncomfortable at any time. Shadow knew how he was with affection and care, and though he had opened it up to him a little bit by playing the role of the person Maxwell deemed his son, it was still quite a fragile topic.
"Well, I think it's great - and y'know, we're still gonna be here, so you can visit any time!" Robyn chimed in, stood beside Maxwell. Shadow nodded at her, and the three began to laugh between one another. Any outsiders could safely assume they were reminiscing over how things used to be when they were all together.
Pumpkin noticed the look on Gatomon's face - and he didn't care. He knew that having no name subtracted definition from who you are. If you were to do something great, nobody could refer to it as yours. Nothing you worked so hard for, would be yours - your achievements would have been up for grabs as people tried to place the accomplishment to the face. A name was so important. Everybody asked "what's even in a name?" but the fact of the matter was, it was all they were. Yes, their inner definition was highlighted with personality that a name could not taint, but it was equally as distinctive as personality and how they acted and thought, otherwise how could somebody cringe at the thought of somebody coming around, or believe good in somebody they had never met?
He simply shook his head. Gatomon was being far too uptight again. Again. He silently hoped she wasn't always like this... he could only take so much. And that applied to everybody - Gatomon was not the first he had met who wasn't prepared to simply sit back and have fun. It was almost depressing.
Robyn nodded her head. "I know he is," she commented ruffling his fur. "I just like to know he's not alone when They're around." she gave Gatomon a smile.