It was Sam’s idea.
Bucky had been holed up in Avengers Tower for a month now, and although his memories were slowly coming back, he was still distant and closed off around everyone bar Steve. There were nights he would scream himself hoarse, and the next day the rest of the team would pretend not to notice the dark circles underneath the soldier’s eyes.
He almost seriously injured Natasha after she went into the kitchen one night to get a drink, not expecting Bucky in there too. It wasn’t until she spoke that he noticed her presence - immediately on high alert and wielding the nearest knife. He would have attacked had he not realised who she was a split second before he buried the blade into the chest of what he had thought was someone coming to kill him.
Sam suggested the idea of a service dog to Steve, and it didn’t take long before he agreed (Stark however, took a little more convincing). They searched around the best available facilities - only the finest for Bucky - before settling on a female Golden Retriever.
At first, Bucky was stubborn. He didn’t need the help, therefore he didn’t need the dog. But Steve was just as stubborn; he refused to get rid of her, and so she stayed. Eventually, he would catch glimpses of Bucky petting the dog when he thought no one was paying attention - the man would immediately become less tense when she was around, and he was more likely to smile one of his rare smiles.
It took less than a month before they were inseparable. Bucky still pretended that looking after her was a chore, but anyone with eyes could see through the ruse. Steve asked him one day whether he’d thought of a name yet - he hadn’t been expecting the cheeky grin that was so reminiscent of the old Bucky to cross his friend’s face.
"Thought I’d name her Peggy. Then I can tease you about how I stole your girl… You’re too slow, old man."
Even though Bucky was joking, Steve knew him well enough to realise that he was paying tribute to another person from their past - the idea that he’d thought of Peggy at all gave him hope for the future.