Есть ли способ указать имя столбца, сгенерированное функцией inline_outer в Spark SQL?

Вам нужно cast вывести from_json и изменить имя столбца:

SELECT 
    id, 
    inline_outer(cast(from_json(campaigns, 'ARRAY<STRUCT<id: STRING, title: STRING, type: STRING>>') AS ARRAY<STRUCT<campaignId: STRING, title: STRING, type: STRING>>)) 
FROM order;

Вот решение, использующее полный pyspark:

from pyspark.sql import functions as F, types as T

# Define schema of the JSON
schema = T.ArrayType(
    T.StructType(
        [
            T.StructField("id", T.StringType()),
            T.StructField("title", T.StringType()),
            T.StructField("type", T.StringType()),
        ]
    )
)
# OR you can use also this schema with your current example
schema = T.ArrayType(T.MapType(T.StringType(), T.StringType()))

# Convert string to struct 
df = df.withColumn(
    "campaigns",
    F.from_json("campaigns", schema),
)

# Explode the array
df = df.withColumn("campaign", F.explode("campaigns"))

# Rename the field
df = df.select(
    "id",
    F.col("campaign.id").alias("caimpagnId"),
    F.col("campaign.title"),
    F.col("campaign.type"),
)

+---+----------+-----+-----+
| id|caimpagnId|title| type|
+---+----------+-----+-----+
|  2|         1| test|  one|
|  2|         2|test2|  two|
|  5|         3|test3|three|
+---+----------+-----+-----+