Ask HN: Support/service desk tools and tips?

I'm an engineer at a smallish company with 5 other engineers. Over the last 3 or so years, we've been focused on developing and selling our software to about ~20 large companies world wide. So far things have been pretty informal when it comes to support. Whoever was responsible for a specific project is the support contact for that project. This means clients have our personal e-mail addresses and sometimes phone numbers. Clients like this, because they know who they're dealing with.

This used to be OK, but it no longer scales. We've now reached a point where some of us are constantly switching between projects in order to provide support. So we're thinking of centralizing and formalizing all of these support tasks.

The first step would be a support@ e-mail address and maybe a phone number which could be rotated to whoever is currently taking care of support. But then we'd need a shared mailbox, or maybe forward support requests to the right person? And the phone number would need to be managed to be directed to whoever is on call. Sounds like a hassle. We have an issue tracker (Jira) which we use to follow up on support on our end, but we've been hesitant to hand out customre logins for Jira given the expense of their license.

How have other growing business handled this growth-induced support phase? Any tips are welcome, as well as tool recommendations to make this easier.