Well I would use aliases, it's a good habit to get into:
UPDATE f
SET [dbo_finance].cusip9 = AssetsC.cusip
FROM dbo_finance f
INNER JOIN AssetsC a ON f.test = a.[IssueName1]
WHERE (a.MinSecClass = 9)
Now that will work fine if the assets table will only return one value for cuspid for each record. If this is a one to many relationship you may need to get more complex to truly get the answer you want.
I see several serious design flaws in your table structure. First joins fields that are dependant as something as inherently unstable as issue name are a very poor choice. You want PK and FK field to be unchanging. Use surrogate keys instead and a unique index.
The fact that you have a field called cusp9 indicates to me that you are denormalizing the data. Do you really need to do this? Do you undestand that this update will have to run in a trigger ever time the cuspid assoicated with MinSecClass changes? Whya re you denormalizing? Do you currently have performance problems? A denormalized table like this can be much more difficult to query when you need data from several of these numbered fields. Since you already have the data in the assets table what are you gaining except a maintenance nightmare by duplicating it?