Dol Amroth; the Elf-haven of Edhellond, was on the borders of this region (the extent of those borders is unclear, but the townships of Ethring and Linhir possibly also bordered Dor-en-Ernil)
Pronunciation
do'rr-e'n-e'rnil ('rr' indicates that the r sound in Dor should be distinctly pronounced)
This land was part of Gondor from the formation of that realm in II 3320. It is harder to say whether the land was known as Dor-en-Ernil, the Land of the Prince, as early as this. If the prince in question was the Prince of Belfalas (which seems likely), then Dor-en-Ernil would have dated back to the earliest times of Gondor. However, if the name referred to the Prince of Dol Amroth, then the name could not have arisen before III 2076, when that line of princes was established.
2
As noted above, it is not definitively established which 'Prince' is described by the name Dor-en-Ernil, but most likely this principality was originally held by the old line of the Princes of Belfalas. In the later Third Age, the Princes of Belfalas were succeeded by the Princes of Dol Amroth. When the Princes of Dol Amroth were established in III 2076, the Ernil (or 'prince') of the land's name may have transferred to the newly-named line, or it might possibly have remained as a historical reference to the old Princes of Belfalas.