How does one choose a sports team to be “their” team?

Most commonly by the geographic area one lives in or has ties to. Otherwise, some people like to choose a team that wins a lot or, on the opposite side, an "underdog" team that never wins.

Like a religion, or culture. As other have said, location, family, etc. Also, advertising plays a role, and then there are people who get really into it and spend a lot of time focusing on different teams, and sports, until they just become team/sport agnostic or focus on the one that meets their statistical, and business practices, requirements.

First step is to forgo a distinct personality.

Geolocation or affinity to location, significant player from region playing at team, family inherited "not ok to not like team xyz", stats, position (underdog, champion) etc

In addition to the other reasons mentioned, I’ll add simply going to a home game for a specific team as an introduction to a sport. For example, I live in an area with multiple high level college sports teams. I went to my first college basketball game at age 11 at one of these schools, so I was their fan for a long time after that. Last year we went to visit the town where my wife’s dad is from. They have a professional team for a sport I enjoy but really only watch at the international level. I had no pro team I follow in that sport, but they were in playoffs while we were there. At that point we didn’t get tickets but I was watching on TV and I enjoyed watching, so I found a way to watch more at home. If we ever go back I’m pretty sure my wife’s cousin will get tickets so we can go. I did get a shirt for the team before we left.

I don't really give a flying fuck about team sports. They tend to bore the hell out of me.

So, depending on the event, when I'm being social and don't mind playing along with sports talk, I've picked teams to tell people that I pretend to be a fan of. I'm honest about it, I say up front that I'm not a big sports fan, and that I don't really care about any team, but I've picked some for the fun of talking about it.

I pick them by mascot most of the time. Currently, my top team is the Baltimore Ravens for US football. The Cardinals for baseball. I flipflop between the Hornets and the Bulls for basketball. I don't run into enough hockey or soccer/football fans to have picked a specific team in either for the US options, though I say I support Arsenal for all other soccer. Why? When I looked up teams, it was the first I ran across.

Any suggestions for a hockey team? I'm open to anything with a cool mascot, or nice uniforms. I won't give a flip about it in reality, but I promise I'll watch them and cheer when it's on.

If it's your city's/country's team, has historically been your family's team, there's a player you particularly like or there's something special that makes the team stand out (eg I support Chivas/Guadalajara becuase they only hire Mexicans). It has little to do with sports, tbh. I know very few people who support a sports team on its sporting merits alone and they're all insufferable.

The correct answer is "the team they first win as in a video game about the sport".

A runner up is "Coolest animal" chosen for mascot. (And no, if a team does not have an animal for a mascot, it is not a viable option. Sorry, thems the rules)

A fascinating discussion when you live in the arse end of Ireland and discover that most people are fans of this team or that team... all of which are English.

A lot of people just choose the closest team to where they live. But I consider that boring and unoriginal. This is different if it's your actual city though. Then it's just city pride. You have to go with it.

As a New Yorker I chose the Miami Dolphins because it's my dad's team and I grew up around aqua and orange. Also most Buffalo people come off as obnoxious dicks that like to break tables like frat boys and I don't want to be around them.

Other options could be as simple as I like their jerseys. They look cool. Because you will most likely wear the jersey eventually.