I wanted to create an instagram account for my site But there is an inactive account with my name?

From help.instagram.com:

''If a username you want is being used by an account that seems inactive, you should consider choosing an available version of the username for your use on Instagram. We suggest adding periods, numbers, underscores, or abbreviations to help you come up with a great available username.''

and:

''Instagram is committed to helping people and organizations protect their intellectual property rights. The Instagram Terms of Use do not allow posting content that violates someone else’s intellectual property rights, including copyright and trademark.''

So if you own a business, you can take legal action action and trademark your name, contact Instagram, and they will delete the account.

There are way too much inactive accounts, but the employees of Instagram don't have time to review them all.

Good luck!