There were no diesel car engines on the domestic Soviet market. Soviet diesels were designed for tanks and army trucks, not consumer cars. I did find a Russian source that says 21045 is using modern (licensed??) VAZ-343 diesel engine made in Barnaul, but it seems the producion of this car is very low, for testing purposes mostly; you can't find it in dealerships outside Togliatti. I'm just too lazy to incorporate lots of this and other useful information available on many Russian sites. Sorry.
The source for the names is the official corporate history of the VAZ, http://history.vaz.ru/cars/ Numeric model numbers like Lada 1200SL were the most used internationallly, and the Soviet "AutoExport Corp." wouldn't be so flexible to appoint different naming schemes for each market, maybe excluding some major ones like the UK. I don't see any point in removing model names. Noone should remember all those crazy manufacturer codes, that's too much for cars that all are based on the Fiat 124 and differ only by say front fascia, like 21063 to 21033.
Don't bother with the Kalina, it's getting mostly mediocre reviews even from the loyal press. The promises were high but the build quality seems to stay on a level typical to VAZ (see The Object of Jokes) and the parts quality is not catching up. The sales of VAZ cars are falling since last year while the sales of foreign cars are increasing, and no further raise of the import tax will help if the VAZ won't improve, but just don't seem to be able to, as shown by the fiasco of their efforts to adapt Chevrolet Niva for export. They'd better license some designs from GM Daewoo, quick, while GM is still not afraid to lose their image once and forever.
I'll be uploading some official imagery from www.lada-auto.ru files some time later.