Our Surname Muntz .
Our ancestors certainly changed the spelling of their surname (Munce)  quite deliberately after leaving Ireland and settling in Australia. No doubt, as was the British custom , the name had been Anglicised by the British officials in Ireland to an English spelling which sounded the same, Munce.

Muntz is obviously the Jewish form of Minter from the following excerpt: Also confirmed  from many  emails  from genealogists on the internet quoting different books on the history of names  it is commonly accepted to be a Jewish name.

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There is a village of Muntzberg [ meaning the "mint hill" I think"] in Northern Germany. 

"Minter is an occupational name  for a moneyer, Old English myntere (cogn. [means kindred names of the same roots]  with German Muntzer, [with umlaut ], Yid[dish]. minster, whence the derivs. listed below). an agent deriv. of mynet coin, from LL moneta money, originally an epithet meaning 'Councellor' (from monere to advise) of Juno, at whose temple in Rome the coins were struck. The Eng.[lish] term was used at an early date to denote a workman who stamped coins; later it came to denote the supervisors of the mint, later it came to denote the supervisors of the mint, who were wealthy and socially elevated members of the merchant class, and who were made responsible for the quality of the coinage by having their names placed on the coins.
Var: Mintor.
Cogns:
French: Monier, Lemon(n)ier.
Italian:Moneta.
Spanish: Mondero.
German: Munzer. [with umlaut]
Jewish: (Ashkenazic): Min(t)zer, Munzer, Min(t)z, Munz, Mun(t)ze (metonymic), Minc (Polish spelling).
Low German: Munter [with umlaut]
Flemish: De Mienter, De Munter, De Muntenaer"

See " A Dictionary of Surnames", Hanks & Hodges, Oxford 

Munce / Muntz  / Bingham Family
from  County Down and Australia and New Zealand
any help please email