"In 1856 a mother registered the birth of her son using only her Surname.Are you saying she didn't give her forename?
"3 Years later in 1859 the mother married and in the 1861 she, her son and husband were listed using his surname. This was repeated in the 1871 census."This would be the choice of the mother & step-father
"In 1880 the son married using his registered name and the Certificate included his mother's original name too." Was the marriage in Scotland?
Was a father named?
"A son born in 1880 was also registered with the original surname."This would make sense as he married by his own birth surname.
"Moving on to the 1881 census the sons new family were listed using his Step Father's Surname not his Birth Surname. This was repeated in the 1891 and 1the 1901 Census documents."Had the step-father died & was the mother living with the family, (maybe a mark of respect although that would seem odd)?
"All the of the 11 children born to the son were registered using his birth surname and his death in 1909 used his birth Surname name too."Seems the correct & normal thing to do.
"So my question is, can anyone see a logical reason for a Step Fathers Surname to be used in the 1881,1891 and 1001 Census Documents rather than his own birth Surname?"Absolutely none, unless as mentioned earlier, if the mother had been living with them, possibly for her benefit but again, it seems an odd thing to do?
Yes to save face in front of the census enumerators and the neighbours.
Save face from what/who?
Surely the neighbours would know them by their proper surname, the surname he was born & married by?
Annie