The thing about LAST from legacy SQL is that the output is undefined for the example that you gave; it doesn't specify how "last" is determined in this case since the input table scan isn't guaranteed to have any particular order. As written, you could express this same query with ANY_VALUE from standard SQL in BigQuery, e.g.:
WITH SampleInput AS (
  SELECT 1 AS id, 'apple' AS name UNION ALL
  SELECT 1, 'banana' UNION ALL
  SELECT 2, 'carrot' UNION ALL
  SELECT 3, 'lemon' UNION ALL
  SELECT 3, 'orange'
)
SELECT
  id,
  ANY_VALUE(name) AS last_record_of_name
FROM SampleInput
GROUP BY id;
+----+---------------------+
| id | last_record_of_name |
+----+---------------------+
| 1  | apple               |
| 2  | carrot              |
| 3  | lemon               |
+----+---------------------+
I don't think that's what you're after, though; if the goal is to get the "last" value based on some criteria, such as the sort order of the name values, then you can use ARRAY_AGG with ORDER BY and LIMIT 1, e.g.:
WITH SampleInput AS (
  SELECT 1 AS id, 'apple' AS name UNION ALL
  SELECT 1, 'banana' UNION ALL
  SELECT 2, 'carrot' UNION ALL
  SELECT 3, 'lemon' UNION ALL
  SELECT 3, 'orange'
)
SELECT
  id,
  ARRAY_AGG(name ORDER BY name DESC LIMIT 1)[OFFSET(0)] AS last_record_of_name
FROM SampleInput
GROUP BY id;
+----+---------------------+
| id | last_record_of_name |
+----+---------------------+
| 1  | banana              |
| 2  | carrot              |
| 3  | orange              |
+----+---------------------+
The behavior of the query is well-defined, and it gives the desired results based on your sample input and output.