How to use jq to create a JSON object

I have the following JSON object:

{
...,
"projects": [
    "abc",
    "xyz"
  ],
...
}

And I want it transformed to:

{
  "abc": {
    "name": "abc"
  },
  "xyz": {
    "name": "xyz"
  },
}

I'm having trouble creating this. I've tried using map as .projects | map({(.): { "name": (.) }} ) but it's not in the format I want and ends up in an array.

You're looking for something like this:

.projects | map({(.): {name: .}}) | add

^{Online demo}

I have a bit of a functional mindset, so I'd reach for reduce here:

reduce .projects[] as $name ({}; . + {($name): {name: $name}})

outputs

{
  "abc": {
    "name": "abc"
  },
  "xyz": {
    "name": "xyz"
  }
}