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$ErrorActionPreference = "Stop"

# get a Core Service client
Import-Module Tridion-CoreService -Verbose:$false
Set-TridionCoreServiceSettings -Version "Web-8.1" -HostName localhost -ConnectionType Basic

$client = Get-TridionCoreServiceClient                              

# get the schema to edit
$schemaId = "tcm:21-4247-8"

$schema = Get-TridionItem $schemaId
$schema.Id

# change the InterestArea embedded component root element name
$schema.Xsd = $schema.Xsd.Replace('type="InterestArea"', 'type="InterestAreaLabel"')
$schema.Xsd

# save the schema
$readBackOptions = New-Object Tridion.ContentManager.CoreService.Client.ReadOptions
$client.Update($schema, $readBackOptions)