The Lubavitcher Rebbe writes in Likkutei Sichos 8 page 361 (at the bottom) that since there was no Navi, and the Rambam (Hilchos Malachim 1:3) requires a Navi (and a Sanhedrin of 71) to appoint a king, Moshiach is not a formal king, rather called one like the Rambam calls Ben Kuzba.
In Likkutei Sichos 23 page 197 footnote 59 he writes that the intention is that he will not initially have the Halachos of a king.
Regarding anointing, the Minchas Chinuch Mitzvah 107 at the end makes a Chakira if the son of a king doesn't need anointing (Rambam Hilchos Malachim Chapter 1 at the end) is because of inheritance or because the anointing of the father continues to the son. According to the view that it is an inheritance, Moshiach won't need to be anointed at all. However, according to the view that it comes through a continuation, since there was a rebellion against the last king of the Davidic line, the anointing doesn't hold just like previous kings who had to be anointed to settle a previously disputed continuation. He concludes that Moshiach will pasken which way to decide this question.
The Lubavitcher Rebbe, however, points out that the very name Moshiach means anointed (and not a possible alternative meaning of greatness), and therefore suggests that there may be two stages where he is initially Moshiach without being anointed, and will then subsequently be anointed.
The upshot is (if I understand correctly - the subject is a bit cryptic and only in footnotes) that Moshiach will initially function as a King, but not have the Halachos of one, and will only subsequently be installed as a proper Halachic king.
See the Rambam at the end of Chapter 5 of Gezeila V'Aveida for how such a "king in function" may work - הסכימו עליו בני אותה הארץ, וסמכה דעתן שהוא אדוניהם והם לו עבדים - The people accept that he is the king, and understand that he is their master and they his servants.