Yes, you can have the Account Name lookup field in the Add Request Form. By Default the Account Name field will not be available and you can enable it in the Request Addition form by following the steps given below.
While creating a new request, if you choose an existing Account (in the Account Name field), you can select only the contacts associated to it in the Contact Name field. However you can also keyin a new contact name and get it created and associated to that existing account on saving the request.
During request creation, if you choose an existing Contact (in the Contact Name field), the account associated to it will automatically get populated in the Account Name field. However, if the contact is not associated with any account (the Account field will remain empty), you can keyin a new Account Name and associate this contact to it upon saving the Request.
Similarly, while creating a request, if you provide a new Account (in the Account Name field), the contact name look up will list the contacts which is not associated to any Account. When a Contact is selected, it would be associated to the new Account on saving the Request.
Also, Account Name would be displayed in the Request list view when it is enabled in the Request addition form.