Carmichael & McCallum of Strathyre

[Stageman]

Have finally linked my grandfather Peter McCallum (b1865) of Strathyre to his natural mother Elizabeth Carmichael (1842-1869) - but - don't know his father as not on birth cert. So my problem is :- how did he get the surname (by the time he was 6yrs and his mother dead)? Was it his 'true' father, if so I have not been able to trace him. My grandfather appeared to be brought up in the Carmichael family according to the 1871 census but then 'disappears' for the 1881 census. Does anyone, from the Strathyre area perhaps, know how I can get to the bottom of this problem?