So they went by their mother's name, not their father's?
There is a David Buchanan, aged 32, born Scotland, shown as what looks like Master (but could be Master of Arts as it's very blotted) of Clare College Cambridge and landholder, living in Harris Lodge, Selborne Road, Clifton-on-Dunsmore, Rugby with wife and several children. In 1871 he is at Northfield House, Newbold Road, Rugby, aged 41, described simply as MA Cambridge. This matches the 21-year-old student in Clare Hall College in 1851. I don't see him in 1881 or later.
He seems to have married Anna Wyndham Penruddocke in Pewsey, Wiltshire, in 1853. Have you got a copy of his marriage certificate? What does it say his father's name and occupation are?
The England and Wales Calendar of Probate says, "Buchanan David of Northfield-house Rugby Warwickshire died 30 May 1900. Probate London 13(?) September to Anna Buchanan widow and George Dalziel writer to the signet. Effects £33654 in the United Kingdom".
A Writer to the Signet is a specifically Scottish designation. There were three George Dalziels who were Writers to the Signet, father, son and grandson. The first died in 1869, and it's not clear whether the one referred to is the son (1843-1926) or grandson (1874-1947), but there is no obvious family connection between them and Todds or Buchanans. I wonder why David chose to appoint a Scottish lawyer with nor obvious family ties to be one of his executors?