The chance that your ancestor's last name is spelled consistently throughout his entire life is slim. The sooner this fact is acknowledged, the better.
What the genealogist should generally look for are spellings that "sound the same" as the intended last name.
It's important to get beyond "this can't be my person because the name is not spelled right." Sometimes there is no "right" way to spell a name, especially if your ancestor was unable to read. Even literate ancestors had their names spelled in a variety of ways. And on top of spelling variations are transcription errors and handwriting difficulties.
So I'm not too concerned if Peter Bieger is:
- Peter Biegers
- Peter Berger
- Peter Beger
- Peter Biegert
As those are reasonable variations. Peter Haase is not.