Use the Nintendo Network ID on multiple 3DS systems

A 3DS system transfer will, as you have mentioned, keep the source SD card as it is, and replace all software and save data of the target.

In addition, eShop accounts will be merged. This means that your digital copy of The Legend of Zelda: A Link Between Worlds will disappear from the target system, but will be ready for re-download, together with all eShop titles you previously purchased. Money in the two eShop accounts will merge, too, and be added to each other. You will, however, have to remove any linked Nintendo Network IDs from the target system.

Source and more information here.

So, I've completed operations as planned and everything seems working as expected. Suppose you want to use new NewName as a primary NNID instead of old OldName with a possible minimum impact.

1. Register a new NewName user on a console, and follow standard procedure of creating new Mii and NNID. You can use same email as for OldName user.
2. Under OldName user, launch eShop and unlink Nintendo Club if necessary.
3. Under NewName user, launch eShop and link Nintendo Club if necessary.
4. Under NewName user, in user switch menu select Make Default.

That's it! You can still access all purchases made under OldName. Of course you lose all information associated with old account, most notably including save games (however some games have shared save files which are user-independent), friends and all Miiverse data. But as long as you keep old user you can always switch back to access it.