Hi
I have got hold of the digital image of the parish register (attached), and he is Thomas on that.
It looks like James on the bishop's transcript, but I think we have to go with the PR as the BT is a copy.
There are a couple of Edmund Breaden baptisms in Pulborough, which is very close to Thakeham and West Chiltington. One in 1715 and one in 1716.
Perhaps one of those is the Edmund Brethen who married Sarah Pell in 1746?