Final answer:
You typically do not need to notify the lieutenant governor of a personal name change, as this is not part of their responsibilities. Their key roles involve legislative duties such as overseeing the Senate and state budgetary processes.
Step-by-step explanation:
The question regarding when must you notify the lieutenant governor of name change appears to be founded on a misunderstanding of responsibilities or processes. Typically, notifying a lieutenant governor of a personal name change is not part of their duties. The lieutenant governor, as described, is a high-ranking official in the government whose responsibilities include presiding over the Senate, casting deciding votes when necessary, and overseeing legislative matters such as the state budget. If the office of the lieutenant governor becomes vacant or they are temporarily unable to act, these duties are carried out by the president pro tempore of the Senate. An example of this position's succession can be seen with the transition from David Dewhurst to Dan Patrick as the lieutenant governor in Texas.