As mentioned in the document at that link, the Irish name Amhlaoibh/Amhlabh comes from the Old Norse name Ólavr/Ólafr (which later became Olaf/Olav/Onlaf/Anlaf) and was popular in areas where Norsemen settled in Ireland. In later centuries, it was anglicized in various ways, including as Auliffe, Olave, and in some places as Humphrey. In Irish, the surname McAuliffe is Mac Amhlaoibh, meaning "son of Olav" (there are a number of Irish surnames with such Norse roots).
Priests often recorded Irish given names in a Latinized or pseudo-Latinized form in baptismal records, or picked a Classical or Biblical name which they thought was a good fit, often without the (often illiterate) parents even having a say in the matter. Some names "stuck" in certain families, such as Cornelius for the Irish name Conor. Others didn't, such as the name Dionysius for the Irish name Donncha (later often anglicized as Denis). Most of Kerry was still Irish speaking in the 1830's, and my guess is that the family called him Amhlaoibh, but the local priest decided to "Latinize" the name as Amlavus, as that article indicates was done in some places. In Irish, the name Amhlaoibh can be pronounced roughly as "OW-luh", "OW-lee", "OW-leev", or "OW-leef" (depending on the local dialect), with the letter combination "amh" becoming the diphthong "ow". In the time when the Norse first settled in Ireland, "m" may still have been pronounced as a consonant, and thus Amlavus would have made sense as a pseudo-Latinized form of the name (the "-us" ending would have been used, because it was common in actual Latin names).