How to convince a Doctoral Committee to accept me as a PhD student when I already have a PhD in a similar field? I have completed my Ph.D dissertation in Pure Mathematics this year  from a relatively lesser known University.
I have been through these questions like Considering a second PhD, this time in statistics. Will any professors be interested in working with me? and Is doing two PhDs a good path?.
However I am interested in pursuing a PhD again in another branch of Mathematics  from a graduate school which is a very well known University.
The University where I want to apply  does not have any age limit for pursuing a PhD.
I want to shift from my current research field to another field as I have become interested in it recently.
I also believe that getting a PhD from top-tier institution will increase my chances for getting a tenure track position.
My questions are:

How do I convince the interview committee that I want to complete another PhD in mathematics/Theoretical computer science as I am genuinely interested.

Also I enjoy remaining a student as long as I can. I enjoy taking courses and writing papers.
Will that be also a valid reason to tell the interview committee.

My advisor feels that my chances of getting another PhD in Maths/TCS are slim since I already have a PhD and the interview committee would consider this as a waste of time and resource to hire me as PhD student again.


The problem is I don't like the fact that I will no longer be a grad student anymore.
I like this whole concept of doing research and getting paid(though meagerly but it still suits me).
If someone could help me with my queries, I will be grateful.
I agree with your advisor that most people would consider that the purpose of the doctorate is to teach you how to be a researcher and another degree isn't going to give you anything you don't already have. And giving the opportunity to another student is a positive good in the eyes of many, possibly most.
Moreover, if your goal is to do research and get paid for it there are better ways to achieve it. You should put your efforts into those instead.
But, to answer your question, about the only way I can think of to achieve this goal is to find someone who has a project and a very specific need for assistance that only you can fill. Possible? Sure. Likely? Not so much. And you would be better off doing a post-doc with them in any case. The pay would be better. You would have an opportunity to learn. Etc.
There is nothing stopping you from learning even outside a formal program. It takes a slightly different kind of discipline, but no more or less than that of a degree program. You can also build a circle of collaborators to help you find interesting ideas that commonly come up in class/seminar situations. You should probably explore that option in any case.