Apparently the H-battleships were supposed to be named after medieval German knights and other heroes, so they'd use a few names like that too.
As you've mentioned, (in the "Table Talks", IIRC) Hitler describes how he does not want any ships to be named after him or Germany, but he was open to ships being named after the medieval knight
Götz von Berlichingen. The thing about that is that Götz von B isn't just any medieval German knight, as the Wiki article linked there reveals. He's something like the German equivalent of the French knights in Monty Python and the Holy Grail. He's famous for saying
Er kann mich am Arsch lecken, "[tell my enemy] he can lick my a**."
I think all vehicles would continue to be named in the
Sd. Kfz. series and the
Pz.Kpfw. series for tanks, with animal names remaining common. There aren't many deviations from the animal names (and I can't recall which of the non-animal names were even official).
Aircraft would probably continue to be named in the same way, with the manufacturer code and a number, although perhaps they would have changed to a system more like the US one in the 60s-80s. That would use J-numbers for fighters (Jäger), probably K-numbers for bombers (Kämpfer), S-numbers for attack planes (Schlactflugzeuge), etc.
If the old system were retained the numbers would be less and less sequential, as there would be a desire to name similar aircraft after famous ones. More so than in other systems, series of the type 707, 727, 737, etc. would appear, because in German the numbers from 21 to 99 are read backwards compared to English. So successors of the Ju 88 might eventually get to numbers like 838, 848 and so on ("eight hundred eight and thirty, eight hundred eight and forty...)
Warships would follow some older naming conventions, but some new ones would likely start. U-boat captains holding the Knight's Cross would be one source of names; perhaps there would be a switch from numbered destroyers to names like
Gunther Prien. There was a pre-war convention of naming civilian ships, but not warships, after Nazis, so I think the names of dead Nazis would be used for KdF passenger ships rather than carriers.
Another category is guided missiles. It's difficult to see Germany developing many guided missiles without designating them in a straightforward way with names like, say, LL-1 (Luft-Luft, Air-Air).