Should i worry if i lied in my new bank that i have no association with another bank when i actually do?

1. It's extremely likely it is just a "stupid marketing question". In this case, answer No and that's it. (For example, in many countries now when you're at a chain store buying a t-shirt or lipstick, when you are paying they say "What is your phone number?" I always say "I do not give it out.")

2. There is a (very) small chance that in your jurisdiction, there is some complicated reporting requirement, along the lines of KYC rules, which means banks are supposed to gather this information. Frankly, it is extremely unlikely anyone would have really in-depth working knowledge of whether this is the case in your jurisdiction (Nepal!).

I'd just repeat that it is extremely likely it is just a Dumb Marketing Question - to which you should answer No, as you did.