Dynamic update statement with variable column names

You can pass the name of the column in dynamic sql:

declare @sql nvarchar (1000);
set @sql = N'update table set ' + @column_name + '= ''''';

exec sp_executesql @sql;

Assuming you want all columns of varchar/char types only (or change the type filter to whatever you need):

DECLARE @tableName varchar(10)
SET @tableName = 'yourtablenamehere'

DECLARE @sql VARCHAR(MAX)
SET @sql = ''

SELECT @sql = @sql + 'UPDATE ' + @tableName + ' SET ' + c.name + ' = '''' WHERE ' + c.name + ' IS NULL ;'
FROM sys.columns c
INNER JOIN sys.tables t ON c.object_id = t.object_id
INNER JOIN sys.types y ON c.system_type_id = y.system_type_id
WHERE t.name = @tableName AND y.name IN ('varchar', 'nvarchar', 'char', 'nchar')

EXEC (@sql)

You can look in the sys.columns table and join on the table name or object_id.

 DECLARE @OBJ_ID INT

 SELECT @OBJ_ID = OBJECT_ID
 FROM SYS.tables
 WHERE name = 'YOURTABLE'

 SELECT * FROM SYS.columns
 WHERE OBJECT_ID = @OBJ_ID

You could use the name field from the sys.columns query as a basis to perform the update on.