HTML auto update select box

So I am writing code for people management webpage. All the result are generated by SQL, now I use Jquery to get result from Java Spring. The problem is I can save it into a JS list and make the update as a function, but I don’t know how I can update my select box.

For example, I got a JS list like this {“tom”,”jerry”}, what I want to have on HTML is enter image description here

and I run the function update() [when clicked a button called “update”]

the list become {“tom”,”jerry”,”spike”}

what I want to have now is enter image description here

so what should I do to achieve this on HTML using tag? Is their any specific data structure to achieve this?

the resource can be used to build this are

a list {"tom","jerry"}
and a function update()