Depending on the wording in your SoW/contract (You DO have a written contract, right??) you may not have to disclose that someone else working for you are doing the customer work.
It may also depend on the structure of your business. I'd talk to a lawyer about it. I am in the same boat as you, and I formed as an LLC, so I've been working on getting other work that I can sub out.
It's legally dicey to represent that you personally will be performing work and then sub-contract to another person. Usually the client won't care. But if things go sideways (especially on a big contract with a lot of money at stake) you are opening yourself to a large amount of legal risk.
Always be upfront and honest. And always negotiate in good faith. The best legal strategy is to never engage in behavior that will require a lawyer to defend.
Please don't attribute anything untoward to me. Reputation is EVERYTHING in this industry. I would NOT suggest someone do something fraudulent, ever.
When you hire $PLUMBING_COMPANY to come fix a leak at your house, you don't care WHO does the work. You want your problem FIXED. YESTERDAY.
So... is it fraud if they send someone who is less experienced than the owner if it's his name over the door, if your problem still gets resolved? No, not at all.
So not knowing OP's details of the contract with $CUSTOMER, you can't assume either way.