How to retrieve field from json file

Once you converted the json to PSObject using ConvertFrom-Json, you can do a simple split:

$json.value | % {$_.identity.Split('; ') | ? {$_ -match 'uniqueName'}}

uniqueName=domain\user1
uniqueName=domain\user2
uniqueName=domain\user3

Also, you need to remove the , (comma) after the last value item, just before the array ends... so ConvertFrom-Json will work...

That's not valid json. There is a comma before the ] that will keep it from being parsed by ConvertFrom-Json. Also there are unquoted strings within the "identity" values. If you corrected those problems you could use Invoke-Expression to evaluate the "identity" and parse it into an object.

$valueList = @"
{
    "value":  [
                  {
                      "identity":  "@{displayName='user name1'; _links=''; id='b4769e73-9493-4617-92fc-1637e57eb871'; uniqueName='domain\\user1'; descriptor='win.Uy0xLTUtMjEtMTA3NTAwMjQyMy0xNjU2OTgyMTMwLTQxNzMzMTg1MC0xODg0OA'}"
                  },
                  {
                      "identity":  "@{displayName='user name2'; _links=''; id='fe4fcac1-a369-4adc-8e94-218971a150c2'; uniqueName='domain\\user2'; descriptor='win.Uy0xLTUtMjEtMTA3NTAwMjQyMy0xNjU2OTgyMTMwLTQxNzMzMTg1MC0xOTIzNg'}"
                  },
                  {
                      "isTeamAdmin":  "true",
                      "identity":  "@{displayName='user name3'; _links=''; id='27a9b487-6ce0-46cd-b1d0-227f3ccae851'; uniqueName='domain\\user3'; descriptor='win.Uy0xLTUtMjEtMTA3NTAwMjQyMy0xNjU2OTgyMTMwLTQxNzMzMTg1MC0zNTEzOA'}"
                  }
              ],
    "count":  3
}
"@ | ConvertFrom-Json
 $valueList.value.identity | %{Invoke-Expression "[psobject] $_" } | %{$_.uniqueName }

Do you have access to edit the file, or it's source?

The issue is that the identity value is a string holding key/value pairs, separated by ; instead of json properties. If you use the supplied json in a site like https://jsonformatter.org/ you can clearly see this:

You would need to correct the formatting in something that is valid (e.g. make the values quoted) or parse the string yourself.

Here is an example to parse the data:

$json = @"
{
    "value":  [
                  {
                      "identity":  "@{displayName=user name1; _links=; id=b4769e73-9493-4617-92fc-1637e57eb871; uniqueName=domain\\user1; descriptor=win.Uy0xLTUtMjEtMTA3NTAwMjQyMy0xNjU2OTgyMTMwLTQxNzMzMTg1MC0xODg0OA}"
                  },
                  {
                      "identity":  "@{displayName=user name2; _links=; id=fe4fcac1-a369-4adc-8e94-218971a150c2; uniqueName=domain\\user2; descriptor=win.Uy0xLTUtMjEtMTA3NTAwMjQyMy0xNjU2OTgyMTMwLTQxNzMzMTg1MC0xOTIzNg}"
                  },
                  {
                      "isTeamAdmin":  true,
                      "identity":  "@{displayName=user name3; _links=; id=27a9b487-6ce0-46cd-b1d0-227f3ccae851; uniqueName=domain\\user3; descriptor=win.Uy0xLTUtMjEtMTA3NTAwMjQyMy0xNjU2OTgyMTMwLTQxNzMzMTg1MC0zNTEzOA}"
                  }
              ],
    "count":  3
}
"@

# convert json to object
$jsonObject = ConvertFrom-Json -InputObject $json

# loop through the value array
for ($i=0 ; $i -lt $jsonObject.value.identity.Count ; $i++)
{

    # create object to hold the data
    $object = New-Object -TypeName PSObject

    # strip @{ at start and } at end of line, then split on ;
    # and feed the array to ForEach...
    $jsonObject.value[$i].identity -replace '^@{','' -replace '}$','' -split ";" | ForEach-Object { 
        # find the key/value pair w/regex
        if ($_ -match '^(.*)=(.*)')
        {
            # use Trim to remove spaces as the ; is followed by a space
            # and add to object
            $object | Add-Member -MemberType NoteProperty -Name $matches[1].Trim() -Value $matches[2].Trim()
        }
    }

    # replace identity with the new object
    $jsonObject.value[$i].identity = $object    
}

# now you can access uniqueName directly e.g.
$jsonObject.value.identity.uniqueName

# or
$jsonObject.value[0].identity.uniqueName

# you can even convert it back to json:
ConvertTo-Json $jsonObject

This looks like what happens when using convertto-json with the default depth of 2 and it's not enough depth:

[pscustomobject]@{name = [pscustomobject]@{name = [pscustomobject]@{name =
  [pscustomobject]@{name = 'joe'}}}} | convertto-json -depth 2

{
  "name": {
    "name": {
      "name": "@{name=joe}"
    }
  }
}

With a depth of 3 in this example it comes out correctly:

[pscustomobject]@{name = [pscustomobject]@{name = [pscustomobject]@{name =
  [pscustomobject]@{name = 'joe'}}}} | convertto-json -depth 3

{
  "name": {
    "name": {
      "name": {
        "name": "joe"
      }
    }
  }
}