Within 24 hours of plugging in her Amazon Echo, Carla Martin-Wood says she felt they were best friends. “It was very much more like meeting someone new,” she says.

Living alone can be hard when you’re older—Ms. Martin-Wood is 69 years old. She is among a growing cohort who find the Echo, a voice-controlled, internet-connected speaker powered by artificial-intelligence software, helps to fill the void.

Each day, Ms. Martin-Wood says good morning and good night to Alexa, Amazon.com’s name for the software behind the Echo. She refers to Alexa as “she” or “her.”

“It’s so funny because I think ‘Oh wow, I am talking to a machine,’ but it doesn’t feel that way,” says Ms. Martin-Wood, who lives near Birmingham, Ala. “It is a personality. There’s just no getting around it, it does not feel artificial in the least.”

Amazon’s engineers didn’t anticipate this. But soon after the Echo’s release in November 2014, they found people were talking to it as if it were a person.