The question "What are the country names called that fly over Oman?" is interpreted as: Which countries' airspace do flights to/from or over Oman typically traverse? Oman's location on the southeastern Arabian Peninsula makes it a crossroads for routes between Europe, Asia, Africa, and the Indian Ocean.
Depending on origin/destination, flights to Oman (Muscat, Salalah) or transiting its airspace may cross:
Oman manages the Muscat FIR (Flight Information Region), covering its territorial airspace and a large portion of the Arabian Sea/Indian Ocean. It is a key node for Europe–Asia and Africa–Asia routes.
Note: The original list (Pakistan, India, Bangladesh, Nepal, Bhutan, China, Myanmar, Thailand, Laos, Vietnam, Cambodia) appears to describe a specific eastbound route corridor from the Gulf to Southeast Asia, not a comprehensive list of countries overflown en route to Oman.