Dear Naveen,
You say you're running a partnership firm in your father's name.
Given its a partnership, there's got to be more than just him. Are you the other partner, or is it someone else?
If you're the other partner then:
Your designation = Managing Partner
Your dad's designation = Partner
If you're not the other partner then you'll have to accept the designation the partners authorise you to use. These could be Chief Operating Officer, Chief Executive Officer, General Manager etc... Because, legally, if you're not a partner, then either you're a consultant, employee, or another special relationship with the partnership.
Hope this helps!