There is not necessarily a single correct answer to this question. Bazaar stores the claimed email address in revisions when they're created, so that people can tell who committed which revisions. If you don't plan to publish the branch in a public location, it does not matter at all really. If you do plan to publish the branch or hope to have the changes merged into an existing public project, the identity provided is how you will be attributed. So it is up to you or the policy governing the project you are contributing to whether or not to use your real name.
Also note, that you can set the identity information on a per-branch basis:
There is not necessarily a single correct answer to this question. Bazaar stores the claimed email address in revisions when they're created, so that people can tell who committed which revisions. If you don't plan to publish the branch in a public location, it does not matter at all really. If you do plan to publish the branch or hope to have the changes merged into an existing public project, the identity provided is how you will be attributed. So it is up to you or the policy governing the project you are contributing to whether or not to use your real name.
Also note, that you can set the identity information on a per-branch basis:
Which ever you like will do. Maybe you would like the same as your Launchpad account in case you use Launchpad.