I'm a freelance programmer (working outside of UK); I'm trying to apply for a UK Business Visitor visa, and I guess the most proper "working status" for my case is "Self employed". However, when I choose this option is tasks me for "The Name of Company/Organisation/Employer", address, etc. What should I fill in, as I don't have any employer and don't own a company?
They have the option to check your employer to see if they are a 'serial inviter' (a party that invites lots of people because they service people who need invitations). They also have the option to check your employer to see if the employer has has been the source of any violations of the immigration rules, like employing people illegally. And finally, they have the right to be sure that any VAT or other taxes that arise from your business visit will be paid.
You are self employed outside of the UK, but do not have a registered company. In this case, you can put your own name and address.
To help them decide upon your application, you should consider submitting any additional evidence that can help convince them that your self employment is legal and that you are accustomed to paying taxes. Such evidence is not a requirement, but may ward off credibility issues. Given the lack of material information about your employer, compliance in your own country is an excellent indicator that you will follow the rules in the UK.