In this context, the name is probably meant to indicate that Daddy Twofoot was a fairly old Hobbit (the name is comparable with the 'Gaffer' in 'Gaffer Gamgee'). On that basis, 'Daddy' was probably not this Hobbit's given name, but rather a title or nickname earned in later life.

'Twofoot' is a real surname, albeit an extremely rare one. Its meaning is difficult to establish with certainty; the most obvious interpretation would be simply 'having two feet', though that hardly seems distinctive enough to identify a particular family. Perhaps a Twofoot ancestor had particularly notable feet of some kind (in the same way that the family name 'Proudfoot' seems to have become established). The alternative explanation would be that members of this family tended to be short, and that 'two foot' refers to their small stature. (In the Prologue to The Lord of the Rings, Tolkien describes Hobbits as 'ranging between two and four feet of our measure', so 'Twofoot' would be a suitable name for a particularly short Hobbit.)