I have changed the built in contact type from Individual to Member. This shows on the contact screen as Member but in the contact reports it still shows Individual. tried to create a new type but it was "based on" Individual" and I had te same outcome.
Another option, and one that will probably make your life a lot easier, would be to use the CiviCRM word replacements feature and simply get the system to translate 'Individual' into 'Member'. Would save any core changes and word replacements wont affect upgrade paths etc.
As per Erik's comments, I wouldn't change the core type.
You should be able to create a subtype called Member. I would not recommend renaming the built in contact type as the CiviCRM functionality will expect it be a around. If you create a new contact subtype, some reports will still show individual as they show the database field 'contact_type' and not 'contact_sub_type'. You would have to change those reports, I would imagine contact subtype might be a selectable field on the report anyway.
Are you looking at the standard CiviCRM reports (and which ones) or do you have customised reports?