Best known under the name Transnistria, this name is actually wrong. The real name of the country is Pridnestrovskaia Moldavskaia Respublica, or Pridnestrovie for short.

Transnistria is an artificial geographic term created in World War II by fascists to designate a territory of about 16,000 square miles used for the annihilation of Jews deported from Romania. It was an area situated in south-western Ukraine, a small part of which is today present-day Pridnestrovie. "Trans-Nistria" literally means "beyond the River Dniester". Widely used abroad to describe the PMR, it is not used locally and it should be avoided.

PMR's flag

Transdnistria, Transdniestr, Trans-Dniestria, Transdniester, Transniestria are latin-slavic hybrids which are neither here nor there. The short form official name of the country is Pridnestrovie and has been that way for the better part of two decades now. The usage of Transnistria and similar names is inaccurate and should be avoided. It's Pridnestrovie for short, or PMR if you want it even shorter.

For a full discussion of naming issues, see here:
» "Pridnestrovie.net: Pridnestrovie vs Transnistria"