Naming a dynamic range

I have a dynamic range such as that in the attached worksheet, which I need to name.
In this situation I usually use offset and counta in a formulation like Offset(G7,0,0,CountA($G:$G),CountA($7:$7)) in the Define Name feature.

This works because the first row and column always are full and start at a given cell (G7)

Unfortunately this will not be true in my present problem. It is the last row and first column which will always be full, but as the range is dynamic I don't know the position of the last row.
I have tried using Offset with the counta of the first column to fix the position of the last row so I can count the columns but I have got in a muddle.
Can any one help with this approach, or perhaps suggest a better way ?

John