how many openings are there and do all of them have names


There are MANY openings
Some of them are named after the chess players who popularized them (like Najorf Sicilian named after Miguel Najdorf). Some are named after places (like London System opening). Some are named after formations (Sicilian Dragon variation is named "Dragon" because the Black pawns resemble the Draco star constellation). There are many more reasons behind certain opening names too. For example, in 1. d4 openings, playing ...Nf6 denotes an "Indian game" so without transposing, we might get a King's Indian Defense, Nimzo-Indian Defense, Bogo-Indian Defense and many more openings. What do all of these 1. d4 openings have in common? Black plays the g8 Knight to f6 in each of them
Are ALL openings named? Not even close
More-or-less most every reasonable opening is named (and many not so reasonable openings too xD) because chess is such an old board game and chances are someone already studied that line before. Chess openings began being recorded around the year 1600 when it was determined White would always move first, so that notation would be easier (before then, White or Black could move first, but if you moved first with Black, then it is identical except everything inverse colors).
Modern openings databases and maybe some books might be closest to labeling knows "openings" and these are all called "book" or "book lines." This term just means it is a named and studied chess opening.
There are 500 ECO codes A00 to E99. Most of these have a name and some of these have more than 1 name.
https://en.wikipedia.org/wiki/List_of_chess_openings