Train service or Train's service - Adj or Possessive (Edit) Genitive
The train service is fine as written. Nouns in English can act as adjectives. Examples:
- Bullet points
- Bilge water
- Boat dock
- Shower head
- Piano keys
These behave more like compound nouns, and eventually they may merge into single words over time. For example, carwash, keyboard, etc.
Service is a noun, you can use it for this meaning as a noun which an adjective comes before it. Some examples are:
- the health service
- the postal service
- the police service
- the prison service