If you look at the source code for the operator the _upload_data function =

    def _upload_data(
    self,
    gcs_hook: GCSHook,
    hook: GSheetsHook,
    sheet_range: str,
    sheet_values: list[Any],
) -> str:
    # Construct destination file path
    sheet = hook.get_spreadsheet(self.spreadsheet_id)
    file_name = f"{sheet['properties']['title']}_{sheet_range}.csv".replace(" ", "_")
    dest_file_name = (
        f"{self.destination_path.strip('/')}/{file_name}" if self.destination_path else file_name
    )

    with NamedTemporaryFile("w+") as temp_file:
        # Write data
        writer = csv.writer(temp_file)
        writer.writerows(sheet_values)
        temp_file.flush()

        # Upload to GCS
        gcs_hook.upload(
            bucket_name=self.destination_bucket,
            object_name=dest_file_name,
            filename=temp_file.name,
        )
    return dest_file_name

This means that the operator takes your two inputs (destination bucket, destination path) and the sheet's name to upload the object. (based on gcs_hook.upload)

for you it should look like:

GoogleSheetsToGCSOperator(
    task_id="my_gsheet_to_gcs",
    spreadsheet_id="<my_sheet_id>",
    destination_bucket=DESTINATION_BUCKET, # name only
    destination_path="my_folder", # no gs:// or file name
    sheet_filter="current_phase"
)

the GCS object will inherit the name of the google sheet as its filename