Eucratideia was an ancient town in Bactria

Bactria

Bactria and also appears in the Zend Avesta as Bukhdi. It is the ancient name of a historical region located between south of the Amu Darya and west of the Indus River...

 mentioned by a few ancient writers.
It was most likely a foundation of Eucratides I

Eucratides I

Eucratides I Megas was one of the most important Greco-Bactrian kings, descendants of dignitaries of Alexander the Great. He uprooted the Euthydemid dynasty of Greco-Bactrian kings and replaced it with his own lineage...

 who is the more important ruler of the Greco-Bactrian Kingdom

Greco-Bactrian Kingdom

The Greco-Bactrian Kingdom was the easternmost part of the Hellenistic world, covering Bactria and Sogdiana in Central Asia from 250 to 125 BC...

 with the name Eucratides. Not much is known about this city and it might be just a renaming of an already existing town rather than a new foundation. Renaming of cities was a common practise in the ancient world.

Location

The location of Eucratideia is disputed. Some proposed locations are:

• Dilbarjin
  Dilbarjin
  Dilbarjin is the modern name for the remains of an ancient town in modern Afghanistan. The town was perhaps founded in the time of the Achaemenid Empire. Under the Kushan Empire it became a major local centre. After the Indo-Sassanids the town was abandoned.The town proper was about 390 x...
  
  
• Ai-Khanoum
  Ai-Khanoum
  Ai-Khanoum or Ay Khanum , was founded in the 4th century BC, following the conquests of Alexander the Great and was one of the primary cities of the Greco-Bactrian kingdom...
  
  .
• Qarshi
  Qarshi
  Qarshi is a city in southern Uzbekistan. It is the capital of Qashqadaryo Province and has a population of 197,600 . It is about 520 km south-southwest of Tashkent, and about 335 km north of Uzbekistan's border with Afghanistan. It is located at latitude 38° 51' 48N; longitude 65° 47'...
  
  ; the 1923 work "The Encyclopaedia Metropolitana: Or Universal Dictionary of Knowledge" states: "Eucratidia, named from its ruler, (Strabo, xi. p. 516.) was, according to Ptolemy, 2° North and 1° West of Bactra." As these coordinates are relative to, and close to, Bactra, it is reasonable to disregard the imprecision in Ptolemy's coordinates and accept them without adjustment. If the coordinates for Bactra are taken to be 36°45′N 66°55′E, then the coordinates 38°45′N 65°55′E can be seen to be close to the modern day city of Qarshi.