Can a divorced spouse of a former veteran recieves benefit if named beneficary at the time of his Death?

It depends on what sort of benefits you are talking about. If you are talking about life insurance that you are the NAMED beneficiary, (the VGLI - Veterans Group Life Insurance) than it matters not who you are... you could be Joe Shmoe from down the street and you would be entitled... The current spouse, if applicable, has no claim to dispute who the named beneficiary is. I hope that helped. If not, feel free to re-phrase your question with further details.

I believe that whomever is listed as the beneficiary is entitled to the death benefit.  I am not sure what comes into play to contest such a designation.