To use the global parameter in your linked service, you'll need to modify the linked service's JSON definition where you replace the hardcoded database name with an expression that references your global parameter. You'll use the @ symbol to denote an expression.
For example, if your linked service is connecting to an Azure SQL Database, and you want to use the global parameter for the database name, your linked service JSON might look something like this:
{
"name": "YourLinkedServiceName",
"properties": {
"type": "AzureSqlDatabase",
"typeProperties": {
"connectionString": {
"type": "SecureString",
"value": "Server=tcp:yourserver.database.windows.net,1433;Database=@{pipeline().globalParameters.database_name};..."
}
}
}
}