In English, the abbreviation aka means "also known as".
A literal German translation might be "auch bekannt wie". Is this, in fact, the correct German equivalent? And is the abbreviation ABW (or the correct one) in common use?
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The direct translation is "auch bekannt als". Alternatively you can use "alias".
I'm not aware of any common abbreviations for either of those (then again "alias" is usually short enough).
Note that "alias" is often used as an adverb (sample from Wiktionary):
Diesen Text verfasste Kurt Tucholsky alias Peter Panter.
Mein Alias beim deutschsprachigen Wiktionary heißt „xyz“.
In case there is not a reference to a person's name (like in the case of an artist name) we can also use "oder" for this purpose:
Ein Parasol oder Schirmpilz ist eine Delikatesse.
To avoid confusion "auch" may be added:
Ein Parasol oder auch Schirmpilz ist eine Delikatesse.
The literal translation would be "Meier, auch bekannt als Müller" or "Meier, auch bekannt unter dem Namen Müller" or "Meier, genannt Müller".
You could also say "Meier alias Müller", but that often implies a cover name with misleading intent, such as for spies.
In case of a woman who has adopted her husband's name, you would say "Meier, geb./geborene Müller"
Except for the "geb.", I am not aware of an acronym or abbreviation for this.