To do a replacement you need to uniquely identify the database row you want to replace. Usually there is an ID column to do that. Does your table have one?
You use the UPDATE thingy, not the INSERT INTO thingy, to change existing data.
If there is only one Kate in the database you can do something like this:
UPDATE my_table_name SET Jobs='Artist' WHERE NAME='Kate'
You want to replace NAME='Kate' with ID=999 if you have an ID column (where 999 needs to be replaced with Kate's actual ID), otherwise everyone named Kate will be turned into an artist.
EDIT:
Ricebowl has a good point if you let users enter this directly free-form. They can put in characters that have special meaning to SQL and do very bad things with your database. Get the basics down first, then spend some time reading about how to protect from "SQL Injection" attacks.
This whole thing is illustrated with one of my favorite comics:
(And see the source blog for more discussion)