Customer and Supplier

If one party is Customer in one transaction and the same party is Supplier in another transaction and we want to maintain one account of every party then what should we do?

You cannot maintain just one account. Customers are subaccounts of Accounts receivable. Suppliers are subaccounts of Accounts payable. To offset sales and purchases, follow procedures in this Guide: Offset simultaneous sales and purchase invoices | Manager.

  1. Actually we are Insurance Brokers, in some business transactions ABC Limited is our
    customer and LMN Limited is our supplier then we use the following entry:
    Debit Credit
    ABC Limited 1000
    LMN Limited 800
    Commission Income 200

  2. In another business transaction:
    Debit Credit
    LMN Limited 5000
    ABC Limited 4000
    Commission Income 1000

What is your point? You asked about an entity that is simultaneously a customer and supplier.

Yes

@Naqvi in your examples:
ABC is a customer 1000 in 1 and a supplier 4000 in 2
LMN is a supplier 800 in 1 and a customer 5000 in 2.

So both entities are simultaneously a customer and supplier.

These are separate ABC/LMN customer and ABC/LMN supplier transactions, and are not mergeable to a single customer/suppler account at the transaction level. To contra the balances between a ABC customer and a ABC supplier then use a General Journal as per the referred to Guide.