You say you're running a partnership firm in your father's name. Given it's a partnership, there must be more than just him. Are you the other partner, or is it someone else?
If You're the Other Partner
- Your designation = Managing Partner
- Your dad's designation = Partner
If You're Not the Other Partner
You'll have to accept the designation the partners authorize 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 have another special relationship with the partnership.
Hope this helps!