Some people drop names to feel important. Others name drop as validation for what they believe. And some throw names around to signify the kind of conversations they are a part of.
As annoying as name-dropping is, it relatively harmless. Unless it is used to influence others. And then it is extremely destructive.
Colleagues who invoke more powerful leaders often do so to turbo-charge their advocacy, turning it from persuasion to requirement. Whenever a colleague suggests the ultimate decision-maker agrees with their stance, they essentially throw down a pair of aces that end the hand.
Highly manipulative colleagues might lie about what others believe, but the truly deceptive actually offer the decision-maker a select set of facts and get them to agree to their position without context. They then get to exclaim forcefully that the decision-maker has spoken and there is little to do but comply.
When colleagues invoke Mount Olympus, so to speak, they influence through mediated power. Their goal is to get things done without an argument and it often works exactly as planned.
But like all power, it is seductive and often betrays people when they depend on it too frequently. In due time, the decision-maker and colleagues learn what is really going on. Once the trust of invoking a name is broken, the credibility of the offender is almost impossible to repair.
As colleagues, we expect to disagree and work through our differences and settle on the best path forward. Any time someone throws a grenade into the discussion by invoking the ultimate decision-maker on the issue, the conversation changes from advocacy to compliance.
When done deceptively, this undermines the goodwill of everyone involved. The best way good leaders avoid this problem is to insist their name and implied endorsement never get used to influence any conversation.
Attending the poker party when they catch a drift that a colleague is using their power to unduly influence others shows everyone the game is rigged. All of the sudden, a good argument looks like a full house.