QUESTION: How to update some records with one value, others with another

I have a list of user records that I need to update once to solve a problem with the application that uses the table.

The records in this table have two fields: name and company.

I need to update the company field with the existing company name in order to get it to appear in the application using the DB.

Some of these have the company set to COMPANY X, others to COMPANY Y.

The question I needed to ask is how can I accomplish updating the records once with the same company that they already have?

For example, would below SQL code work:
update user_records_table
set company=company Received on Thu Sep 10 2009 - 00:02:46 CDT