I would suggest that a naturalized player would hold "two citizenships" - of a mother country and of a country which naturalized him. This way, that player could help boost merchandise sales of clubs from both countries. Also, that player would be able to play for any of those two NTs, however, once he plays a match with one NT, he's not eligible to play for other NT anymore.
It would be just like in the real world under FIBA rules.