Is it same as the name 'Rama' which we use in daily life?
From the Upanishad itself, 2nd Adhyaya:
वन्हिर्नारायणो नाझड्यो जाठरः केवलोऽपि च ॥ ६॥
द्व्यक्षरो मन्त्रराजोऽयं सर्वाभीष्टप्रदस्ततः ।
Vanhi (र) coupled with Narayana (आ) and the Jathara (म) alone make up the two letter mantra (राम) which is the king of mantras that fullfils all the desires within one'...
Ayodhya's tirtha-sthala (holy spots) like the exact location of Shree Rama janma-bhoomi, Rishi Lomasha ashrama (hermitage), Vasishtha-kunda, Brihaspati-kunda, etc. which are mentioned in ancient scriptures all exist in present-day Ayodhya [Ref: Skanda Purana 2.8.1-10].
God Rama killed Tadaka and they reached Rishi Vishwamitra's Siddhashrama, at present-day ...