Brecon is the English, or Anglicised, name which is found on all atlases etc.
Aberhonddu is the Welsh name, which is very easy to understand as 'Aber' = 'mouth of the river' so in this case 'The mouth of the river 'honddu'.
'Honddu' itself means 'black place'
This is a very rugged and dramatic part of Wales with its associated mountain range 'The Black Mountains' (Y Mynyddoedd Duon)
The name 'Brecon' comes from Brycheiniog, one of the Early Middle Age kingdoms of Britain situated in what is now the southern part of mid-Wales.
Apart from the Black Mountains to the south-east of Aberhonddu, the Bannau Brycheiniog (Brecon Beacons) National Park extends to the south and west, including the highest hills in southern Britain.
Nice area to live in!