There are plenty of examples of updating a value in a nested entry in jq, but I think I have a unique question, because the value I want to provide is already in another part of the same entry.

Given the following input:

{
  "items": [
    {
      "name": "first"
    },
    {
      "name": "second"
    }
  ]
}

I want to produce this output:

{
  "items": [
    {
      "name": "first",
      "value": "first"
    },
    {
      "name": "second",
      "value": "second"
    }
  ]
}

In other words, I want to copy the value of .name to the value of .value for each entry in items[].

Assignment is easy enough if the value is static. jq '.items[].value |= "x"

But since the value is dynamic, I always get stuck either at the wrong context level:

$ jq '.items[].value|=.name' <<< '{"items":[{"name": "first"},{"name": "second"}]}'
{
  "items": [
    {
      "name": "first",
      "value": null
    },
    {
      "name": "second",
      "value": null
    }
  ]
}

Or with the wrong output context:

jq '.items[]|(.value=.name)' <<< '{"items":[{"name": "first"},{"name": "second"}]}'
{
  "name": "first",
  "value": "first"
}
{
  "name": "second",
  "value": "second"
}

How can I make the change within the entries, for each entry, but still output the whole thing from the top level?