A CTE is just a temporarily-created relation (tables and views are both relations) which only exists for the "life" of the current query.
I've played with the CTE names and the field names. I really don't like reusing fields names like id in multiple places; I tend to think those get confusing. And since the only use for names.id is as a ORDER BY in the first ROW_NUMBER() statement, I don't reuse it going forward.
WITH namesNumbered as (
select myId, Name,
ROW_NUMBER() OVER (
PARTITION BY myId
ORDER BY id
) as nameNum
FROM names
)
, namesJoined(myId, Name, nameCount) as (
SELECT myId,
Cast(Name AS VARCHAR(225)),
1
FROM namesNumbered nn1
WHERE nameNum = 1
UNION ALL
SELECT nn2.myId,
Cast(
Rtrim(nc.Name) + ',' + nn2.Name
AS VARCHAR(225)
),
nn.nameNum
FROM namesJoined nj
INNER JOIN namesNumbered nn2 ON nn2.myId = nj.myId
and nn2.nameNum = nj.nameCount + 1
)
SELECT myId, Name
FROM (
SELECT myID, Name,
ROW_NUMBER() OVER (
PARTITION BY myId
ORDER BY nameCount DESC
) AS finalSort
FROM namesJoined
) AS tmp
WHERE finalSort = 1
The first CTE, namesNumbered, returns two fields we care about and a sorting value; we can't just use names.id for this because we need, for each myId value, to have values of 1, 2, .... names.id will have 1, 2 ... for myId = 1 but it will have a higher starting value for subsequent myId values.
The second CTE, namesJoined, has to have the field names specified in the CTE signature because it will be recursive. The base case (part before UNION ALL) gives us records where nameNum = 1. We have to CAST() the Name field because it will grow with subsequent passes; we need to ensure that we CAST() it large enough to handle any of the outputs; we can always TRIM() it later, if needed. We don't have to specify aliases for the fields because the CTE signature provides those. The recursive case (after the UNION ALL) joins the current CTE with the prior one, ensuring that subsequent passes use ever-higher nameNum values. We need to TRIM() the prior iterations of Name, then add the comma and the new Name. The result will be, implicitly, CAST()ed to a larger field.
The final query grabs only the fields we care about (myId, Name) and, within the subquery, pointedly re-sorts the records so that the highest namesJoined.nameCount value will get a 1 as the finalSort value. Then, we tell the WHERE clause to only give us this one record (for each myId value).
Yes, I aliased the subquery as tmp, which is about as generic as you can get. Most SQL engines require that you give a subquery an alias, even if it's the only relation visible at that point.