If it is a given name or nickname, it will need to be lenited, i.e,
a Mhiadhachlughain.
If it is a family name/surname, then it is incomplete. Is it meant to be an old form of McLoughlin or something?
I think the modern form of "McLoughlin" is
Mac Lochlainn. Now, when talking about someone called
Mac Lochlainn you can use a noun form
an Lochlannach (in this case it reverts to the noun
Mac Lochlainn is derived from, i.e.,
Lochlannach is a "Scandinavian; Norseman".)
The family name of someone called "McLoughlin" changes depending on their gender and marital status (but only if female

):
Mac Lochlainn (male = "Mr McLoughlin")
Nic Lochlainn (female, unmarried/maiden name = "Miss McLoughlin")
Bean Mhic Lochlainn (female, married to Mr McLoughlin = "Mrs McLoughlin")
To address them:
A Lochlannaigh† "Mr McLoughlin" (vocative)
A Iníon Mhic Lochlainn "Miss McLoughlin" (vocative)
A Bhean Mhic Lochlainn "Mrs McLoughlin" (vocative)
(Corrections welcome.)
†Question for other translators: If the name were one with Ó such as Ó Lochlainn (Loughlin), then there is another form A Mhac Uí Lochlainn for addressing him, but what happens when the name starts with Mac? A Mhac Mhic Lochlainn? or simply A Mhac Lochlainn?