Indios: Surnames

[makas@...]

When the Spaniards made converts of the Indios of Mexico they gave them 
Spanish names. So am I correct that there are peoples of every Spanish 
surname out there that can eventually trace their genealogy back to 
where that name was "assigned" and then the trail would end because it 
would be extremely difficult or impossible to find a written record of 
the Indio names before conversion. . .OR. . .or do I have this all 
wrong? Was it only first names that were assigned to them and then as 
the Spaniards crossbred with the Indios those bi-racial children then 
had a ligitimate [traceable] name that could be traced back to Spain?
How exactly did the names for the indios come about?

joseph