robin01, if you don't want to replace the data already in the database, then you should use INSERT rather than UPDATE.
Insert will add a completely new row to the database with the provided data.
If however, you want to append to the data already stored in the field you can use the concat() to do so (in MySQL at least):
That would add "Mr. " to the start of the name of the person with ID number 1.
UPDATE test SET name = concat("Mr. ",name) WHERE ID = 1
Edit: had to fix my incredibly bad example