"I would have been an archaeologist"
how can I say this in other words? and is it true in blue written?
===Not a teacher===
If I were the son of Kathleen Kenyon, I would\might have been an archaeologist.
The above sentence is a third conditional statement. Your sentence alone is incomplete.
"I would\might have been an archaeologist" = Independent clause.
"If I were the son of Kathleen Kenyon" = If clause.
When you say "is it true...", do you mean "Is it correct?". We have no idea if it's true (a fact) that you would have been an archaeologist - only you know if this is true!
As far as your question is concerned though, what you have written is not a complete sentence. You need more information, for example:
I would have been an archaeologist if I had studied archaeology at university.
You can also say "I could have been an archaeologist if I'd studied archaeology".
Saying "would" suggests that you are quite certain that that would have been your job had you studied archaeology, whereas using "could" suggests that this would have been a possible job.