Part of the Bond mythology is that he was an orphan (family died mountain climbing), that, along with his lifestyle means he has nothing to hide, so doesn't use an alias.
Also his reputation is such that he wants the villain to know who he is to intimidate him.
For example in Casino Royale
Le Chiffre: Mr. Beech, or is that Bond? I’m a little confused.
Bond: Well, we wouldn’t want that, would we?
There is also a school of thought that Bond is the CODE NAME, and the continuity is maintained across the movies as there have been a number of Bonds over the years, and the name is maintained for MI6's best agent due to the reputation.
This is suggested by quotes (Lazenby saying "this never happened to the other guy") and by actions (Brosnan Bond is left with Jinx and a big box of diamonds, but is not contacted by M in the usual bedroom embrace.
Also by out-of-time objects:
- The Connery era gadgets in Die Another Day
- The Goldfinger DB5 in Skyfall/Spectre, which has the BMT216A numberplate, so isn't the Casino Royale one.