This is a rather pedantic question and the only reason I ask is because something sounds wrong to me.
Say someone is giving instructions to a person to write down a name they used to go by but no longer do. Which phrasing is most correct?
Write down any previous names you have.
Write down any previous names you had.
Write down any previous names you have had.
The first one seems most logical to me. The statement is assuming the person may currently have a previous last name. The second one seems logically wrong, as it's saying the person used to have a previous last name (maybe person reverted back to original name).
Changing the context to a similar structured sentence, to my ear using "had" is clearly the correct choice:
Tell the dentist of any previous infections you had.
Here, replacing "had" with "have" certainly would be wrong.