Hi Pramodh555,
As a BA Manager, I read this with interest. Telling someone to change their title because they don't have the money to pay for your proper role is an old, and I personally think, below the belt tactic.
I'm not sure if you have accepted their offer yet, but if I were you I would do/ask the following:
1. Get them to create a job specification for your role (if they haven't already). It should outline what your day to day responsibilities are.
When you get this, does it read as if you were a BA? If it does, then ask yourself are they trying to hire a BA, but on the cheap? If you are doing more, why aren't they paying you more? Ask yourself what this tells you about the company?
2. What is your salary requirements and what are they offering. If they are using these tactics now, they wont suddenly say 6 months down the line "Oh, do you know what, you are a BA aren't you - here have a BA salary". You will always be behind on that front.
3. What is your career progression. Ask them directly. IF you have created a niche role for yourself, then the chances are you may find it hard to get out of that niche.
4. If you are looking to leave in the next 5 years, make sure your title is a bit more 'progressive'. By that I mean the following. Place yourself in the minds of another company that might want to hire you for a more senior role (assuming you want to go for one in the future). Are you more likely to get hired if you are a "Requirements Advisor" or a " Requirements Manager"? Obviously the 'Requirements Manager' (I'm not suggesting these as titles for you, more just an example). So maybe think about what looks better on your resume. After all, if your new hiring company cant be bothered to think of a title, why not think of a better title for your own personal ambitions?