Hi, hope everyone is well and safe at the moment.
I have a wee question that occurred to me at 3 am one night that's been driving me mad.
My surname is O'Mahoney which I know is derived from the old Mathghamhain but we've always pronounced it as something similar to "Mahgowin" which I've realised recently probably isn't the case. This sent me into a panic thinking I've also been pronouncing Ní Mhathúna incorrectly so I thought it would be a good idea to ask what everyone thinks about Mathghamhain and Ní Mhathúna.
If anyone is good with IPA, that would be fantastic. Also, I'm from Munster so I'm afraid Ulster pronunciations won't be very helpful to me
Thank you so much!

[ˈmˠahɣəwənʲˈ] from this Wikipedia page about the early modern 16th poet: https://en.wikipedia.org/wiki/Mathghamh ... rn%C3%A1in

I think, from what you wrote above, that your pronunciation is not too far off if not spot on.

I have a friend who pronounces his family name Ó Murchadha (now Ó Murchú) as "Oh Murcada" which is really not correct at all.

When correct?

Pronunciation changed over time (and spelling, too).
Modern Irish Mathghamhain in refomed spelling Mathúin /mahu:n´/, genitive Mathghamhna / Mathúna /mahu:nə/

In former centuries gh and mh were pronounced as such (/γ/ and /v/) not only word-initially (as often today)
And th once was like English th, nowadays just /h/
So Mathghamhain perhaps once was /maθγavan´/

The original Mathghamhain (ancestor of the Ó Mathghamhna) died 1017, so th was already /h/ at this time.

And again thousand years ago it was perhaps "Matogamunis" or similar (just a guess).