Now to get from SN7404N to SN74AUP1T04DCKR:
SN74 is still the same
AUP gives you 1.8V logic, this "naming component" goes back to the 70s/80s with 74S
1 gives you a single gate rather than 6 of them. You should be ignoring these if you're looking for the 6-gate variant.
T gives you level-shifting capability. You should be ignoring these if you're looking for a "normal" chip.
04 is from the original 7404 name, for an inverter.
DCK replaces the N, indicating a SC70 2mm × 1.25mm SMD part
R is not part of the part number, it's an ordering specification for a specific reel size. You should be ignoring this while designing, until you need to worry about delivery details.
> all this adds up to finding parts being very annoying when building stuff
idk, I've never had problems due to naming schemes. Parametric searching is IMHO where things become painful.