You can issue bills to any one without requirement of tax registration or company registration.
For instance I provide services and issue bills with my firm name. Though it is not a registered company. A registered company means company registered with ROC.
For a small level business you need not to register a company, you can provide services in your individual names also.
Your PAN number is sufficient to file your income tax returns and run your business.
Now coming to Billing part.
There are 2 type of bills, one is normal Invoice and another a Tax invoice.
Normal invoice is one where you do not charge any Tax in invoice. In Tax invoice you will be charging tax on amount of service provided.
You need to issue Tax Invoice if you are registered under GST. Many MNCs and big companies do not deal if you are not registered under GST.
Registration under GST is optional and you need to compulsory register if your receipts/turnover in a year cross 20 lakhs (for special states limit is 10 lakhs).
You can issue bills to your clients without charging GST, if you are not registered. Format of bill will be normal Tax invoice except you need not to mention as Tax invoice but Invoice in heading and do not charge any tax.
You can try Billing Software by KnowyourGST.
If you are going to register for GST, then you can create GST Tax invoice using above mentioned application. Or simply issue Bill of Supply if you are not registered.