I don't know anything about your lineage but this is some information which hopefully can help you..
I doubt the enumerator should've written BYREN. What was most likely was BAYERN which is BAVARIA in Germany.
To learn more about genealogy from that area you can look at:http://www.genealogienetz.de/genealogy.html
Niederbayern (Lower Bavaria)
Oberbayern (Upper Bavaria)
There are also these message boards:
Boards > Surnames > Klahr
Boards > Surnames > Klare
and I'm sure there must be one for Bavaria and also Germany which might be helpful.
From one of the surname message boards this was written:
"A passage in Rex O. Matthews book on KLAHRs
reads: The phonetic misspelling were usually
created by census takers, county clerks, and
others who delt with the German-speaking
'...had his last name spelled differently
on different records, Clawr, Glar, Klar, Klare,
Klarr, Klaur, Klaar'.
Good luck in your research!