Greek for John 3:3: ἀπεκρίθη Ἰησοῦς καὶ εἶπεν αὐτῷ Ἀμὴν ἀμὴν λέγω σοι, ἐὰν μή τις γεννηθῇ ἄνωθεν, οὐ δύναται ἰδεῖν τὴν βασιλείαν τοῦ θεοῦ.
One verb that John uses in 3:3 is γεννηθῇ (aorist subjunctive passive) coupled with the adverb ἄνωθεν (evidently meaning "born from above" or "born again"). But when I research γεννάω alone, I have yet to find a place in Scripture where that verb itself means "rebirth" or "regeneration." Of course, one could argue that γεννηθῇ ἄνωθεν possibly conveys the sense of "regeneration" and maybe this much is true. In fact, Peter's words at 1 Peter 1:3, 23 evidently deal with the same process that John does in his Gospel. And in his first Epistle, Peter does refer to a "new birth" or new begettal.
So if one wants to call spiritual rebirth "regeneration," maybe there's nothing wrong with using that kind of terminology to describe the marvelous divine process delineated in John 3:3ff. But it could be more appropriate to call divine justification, "regeneration." Compare Titus 3:5-6.