Hi-
Yes, you can do both of these things.
To keep the original attachment, use the parameter /clear=no
To name a file, you can use the parameters /name (non repeating) or /namexpath (repeating attachment).
In your case you'll have to add form name to each row of the schema, so you could use
SaveToSharePoint /url= /xpath=/my:myFields/my:group1/my:group2/my:File /clear=no /namexpath=my:name
Hope this helps!