Sometimes this is called a celebrity handler or wrangler (I've especially heard these terms in the context of Hollywood, but they might be used elsewhere).
Here is a description of celebrity handler from the blog of someone who has held the job:
Most recently, I picked up the job of official celebrity handler. I don't want to call it an "assistant" job because it makes it sound more permanent than it is. As a handler, it is my responsibility to make sure that the celebrity gets from point A to point B on time with relative ease and no problems. I handle crowds, questions, and generally make sure that the celebrity has whatever he or she might need while in my custody.
That sounds very like your meaning, but note that some celebrities/VIPs do have permanent "handlers" on-staff (though they usually have a different, more formal title, like "agent" or "stylist").
And celebrity wrangler, from Blumenfeld's Dictionary of Acting and Show Business:
A person who works for the organizer of a publicity or other gala social event and whose job is to arrange for the appearance at the event of a well-known star or other famous person. The wrangler also arranges for transportation and other needs, and looks after the celebrities once they have arrived.
Note that wrangler has a bit more connotation that the person might be involved before the event in the actual scheduling, and sometimes the term might mean someone who actually recruits the celebrity/VIP.
Finally, a more general-purpose term is gofer. From Cambridge Dictionary:
a person whose job is to take messages or to collect and deliver things for other people
This one apparently comes from the phrase "go for" as in "go there to get something", because the gofer is always being told "go for this, go for that". It doesn't necessarily imply a VIP boss or temporary position (a regular, not-very-important office might employ a permanent gofer) but could certainly be used in your context.
