Can anyone name this plant?

some kind of phormium maybe

Looks like phormium to me too.

I suggest thinning the leaves, there are too many for the root system, thats why they are browning, I should remove all browning leaves.

I find my phormiums always have a few leaves turning brown over the course of a season even though I thin them in spring - I think it's something they do naturally

Phormian

I agree with the others, it is a Phormium Tenax or New Zealand Flax. The best way to keep it looking at its best is to trim off the dead leaves at the base. I don't wait til spring like Andrew, as I am too impatient to make it look nicer! They seem to respond quite well to fairly regular pruning.