There are many reasons why you should accept and should not accept the managing request.
I want to be only one manager for my profile
Don't accept the managing request.
I want to let my profile be managed by the user who sent me a managing request
Accept the managing request. But then you will not get the inquiries anymore for that profile.
I want to let my profile be managed by the user who sent me a managing request, but I want to be a manager too (get the inquiries) for that profile
Accept the managing request. But then submit a managing request to yourselft (your profile) too and accept it. If you don't have that option you probably don't have created a Manager/Agency profile type. Create a Manager/Agency profile first and then submit a managing request to your profile and accept it. In that case you and all other managers will get the inquiries depending on which one will other user choose. One profile can have many managers and other users can choose which one they want to communicate with.