Always cite a source using the data given in the source. This is a simple rule and it always applies, without exception.
In your reference list,
- do not change names of places that have been changed in later times,
- do not give the real name of an author if the book was published under a pseudonym
- do not change the name of an author who has married and later publications appear under a different name
- do not change a publication year given in a source even if it is wrong (e.g. if the volume of a journal for a certain year was actually published at a later date, as is quite frequent; if neccessary, you may do:
1943 (published in 1944)
)
If for some reason it is necessary for the reader to understand these changes, you may explain them in text (e.g. Smith-Hartman (publishing as Smith, 2010) ...
). But it rarely is. The sole purpose of a citation is to credit your source in a way that makes it possible for others to find that source. Not to explain historical facts.