"Changing a legal name" is a legal process and the result, a new name for the same person, is no more a lie than choosing a nickname for oneself. From a legal standpoint, the changed name is now a legally permissible "lie."
This does not result in mistrust by a court because the legal system was involved in the change. Of course, all this assumes the "change in legal name" went through the legal process.
Actually changing your "legal name" in many places isn't a "legal process" at all. Not if you mean a state-managed, form-filling exercise.
In the UK for example the law only specifies you must make a public declaration of your intent to use a new name (a notice in a local newspaper will do), and then completely abandon any all use of the old name. Even the venerable old 'Deed Poll' service is just a mechanism to make that initial declaration, it's actually a private register.
In the U.S. anyway, you have the right to use any name by which you represent yourself consistently without intent to defraud, much akin to a common-law marriage.
This does not result in mistrust by a court because the legal system was involved in the change. Of course, all this assumes the "change in legal name" went through the legal process.