In an eval statement, strings have double-quotes ("string") and field names have single quotes ('field name'). So do this:
eval STRINGBACK=[search source="FILE.csv" host="HOSTSERVER" sourcetype="csv" 'COLUMN NAME WITH SPACES IN CSV'="123" | table "COLUMN NAME WITH SPACES IN CSV"]
Or better
rename "COLUMN NAME WITH SPACES IN CSV" as new_name
and then just use the new name everywhere.
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