Callum Logan

[Dazzle]

From Wiki: 'In accordance with the official ITV website, David is listed as Max's adoptive father. Although the adoption has been discussed in previous storylines, this has never been confirmed onscreen. The character continues to be credited with the surname "Turner". '

So, as clear as mud then.

I think we'll just have to accept that although David and Kylie agreed that he should adopt Max they never actually got around to doing so (unless we're given another explanation).