Snake is their true name, period.
Solid Snake: I have a name.
Liquid Snake: NO. We have no past, no future. And even if we did, it wouldn't truly be ours!
They're product, their tools, they were designed to be an insurance policy. Why is this so hard to understand?
that is the fact, or how Liquid sees it? i mean Lebron James nicknamed The King, so which one is the real deal? From other people's point of view, it depends on which name was registered on his official papers, but to Lebon The King himself, he might see The King as his real name?
but in the end, whether it's Jack Snake, David Snake, Classified Snake, George Snake or the other Jack Snake, all the Snake codenames/realnames as you see fit are given under the Patriots authority including Naked Snake back when Zero was in FOX, whom later became the leader of Patriots, which was probably his ideas for giving out all the Snake codenames.
i can see the prejudice on Raiden, despite many likes him (or don't despise him), takes it as an insult to Big Boss & his 3 sons for being seen as a Snake.
Zero in FOX gave Big Boss Naked Snake
Patriots gave Solid, Liquid & Solidus the "Snake" based on inheritance to Big Boss
Patriots GW AI gave Raiden his codename Snake the same way Zero gave Big Boss "Snake". And the fact of all people Solidus decides to adopt a kid named Jack means there's something about the name. I'm sure if it weren't for all the confusion Raiden wouldn't have been called Raiden and instead kept the codename Snake for the rest of the series.
So in short: Big Boss & Raiden were given codenames Snake for their missions
Solid/Liquid/Solidus were given codename Snake based on their relationship with Big Boss the original Snake.
i see no way once can dismiss Raiden was never a snake. this is all i will be writing about Raiden' was also once a Snake.