Lets not get too focused on my game versus your game. I was just pouting out that nothing actually changes, mechanically. If your table enjoys a different name, cool, but lets not pretend you're making actual changes to the game.
I disagree.
An ability named "sneak attack" in my game, is an attack made against an unaware opponent. If the opponent is aware of the rogue, the ability doesn't function - which is why I renamed it. If a player wanted the sneak attack ability, I would gladly allow it. Each ability must represent something in the fiction. If that ability is nonsensical in the function, the mechanic doesn't active (in my game).
When a character games an ability in my game, I ask the player what it means. The player then explains the how the ability acts in the fiction and mechanical implications of that description. If the player isn't satisfied, the player can choose a new description or we can house rule a new ability.
That way, even character ends up a little different. No two rogues are the same - in fluff or mechanics. Every character is unique.
I'll give you another example, a halfling who describes his sneak attack as piercing vital organs would not be able to "sneak attack" (regardless of the ability's name) a slime and would have to make an athletics check to first climb a giant in order to reach his kidneys.
For that reason, I would generally advice a halfling to choose a different description of the ability, because each description does, in fact, result mechanical differentiation.