JoinAcross question with combined keys

Unfortunately, JoinAcross does not presently (V11.1) support any form of computed key specification. We have no choice but to adjust the first dataset to include the full name.

We do not necessarily have to go so far as to destructively alter d1 -- we can add the computed column in an inline query:

JoinAcross[
  d1[All, <| "fullname"-> #first~~" "~~#last, # |> &] // Normal
, d2 // Normal
, Key["fullname"] -> Key["fullname"]
] // Dataset

---

As an aside, in later versions of Mathematica we can usually omit the applications of Normal, Key and Dataset:

JoinAcross[
  d1[All, <| "fullname"-> #first~~" "~~#last, # |> &]
, d2
, "fullname" -> "fullname"
]

... but be prepared to add them back in since JoinAcross has been very finicky across releases (especially when applied to datasets).