We might be conflating a number of special uses of the first person plural. For example, there is the 'royal 'we'', royal because of its use by Royalty. The recently late Queen Elizabeth always used it in her public speaking. Originally, it was because the monarch wasArguably, that 'royal we' gets taken up by all sorts of leaders at all sorts of levels of a variety of organisations and institutions. Until perhaps the early to mid 18th century, the monarch was speaking for him/herself on all matters of state. If you attend carefully to the speeches of recent monarchs, they have been careful to separate 'We', to refer to the royal household, of which they are in charge, and, in the case of the late queen, 'My' when speaking of the one individual role of appointing the leader of any UK government.
So most uses of the first person plural to refer the singular person speaking can be described as a 'royal we' in a pejorative sense of arrogant or 'stuck-up'. We think "who do 'they' think 'they' are?". That will be so, unless the speaker is explicitly the spokesperson of some group of people.
What can happen is that a strong leader comes to use the 'royal we', referring to her personal opinions and decisions when she is supposed to be the government leader, delivering corporate rather than personal decisions.
So there is no need for a special word. It exists: 'the royal we'.