How do you deal with legitimacy?

I've been through this before (although with a bigger team) from both sides of the table. Firstly, you should understand and mentally reframe what they evaluating. 9/10 this is not a challenge on your "legitimacy", it's an assessment of your medium-long term viability, potential trajectory from a risk management perspective. And any competent company is 100% correct to do this in a b2b setting.

It's important to be honest with the client, and discuss the clients concerns so that you know whether they are immediately addressable to land a deal, or if they are something you may need to factor in for future business development within that market segment. For example, in my previous experience, the client concerns were over business continuity in the event of a vendor failure. We were able to successfully mitigate this concern and land multiple deals by doing things such as implementing SLAs, sharing product roadmaps and team structure, and technology escrow agreements. A word of caution, there's a lot of overhead involved in this and it should only be considered for enterprise deals.

In your case, you need to try and understand the client better. Are they concerned with business continuity? Reputation harm? Custody of funds? Something else? Talk to the client and find out.

I always use the royal "We" when I talk about my team of one. :D

In SaaS it is a numbers game. A few odd ball customers does not make a business.

I think envy often plays a role.

Lots of good comments in here.

What I think the client is also looking for is just assurances you aren't going to disappear. They are going to invest their time, energy, and even some personal dependency in your product. Sort of like asking if someone is looking for a serious relationship on the first date.

The last thing they want is for the product to just disappear one day.

In the early days I've often cited my commitment and previous track record in building systems and software. I also acknowledge that I understand they are taking an early bet and try to give legitimate assurances for their concerns.

I had a friend that put up the code in a private repository as a failsafe that he would give them the code if he went out of business. He even put that in a contract.

Don't take it personally if they don't want to take the risk. If they don't, ask if you can contact them in 3 months or so, then actually follow up on it.

There have been very few cases in which a prospect or an existing client has asked about the team behind my product. I would always answer with "a very small but dedicated team".

Not for one moment I have given them the impression that there's just one guy (me) behind the product, even though for 1 year out of 3 that I've been in the market, I did have a team of size 4.

As long as you deliver a great product and a great customer support, I don't think your prospects / clients would care whether there's 1 person or 100 people behind the product.