According to The Wrestling Observer, WWE does indeed plan on bringing Shinsuke Nakamura to the main roster at some point, and the company is using NXT as a transitional trajectory for the former NJPW star. Nakamura’s first WWE match will come at NXT Takeover Dallas against Sami Zayn.
With regards to his theme music, there were rumors that WWE purchased the rights to Nakamura’s “Subconscious” theme song he used in NJPW, but that is not true.
As far as his name goes, it should be noted that just because he is using the Shinsuke Nakamura name in NXT, that does not mean he will keep the name if and when he makes his main roster debut.