Have you looked into whether there are any city or county regulations regarding running a business under an assumed name? It's required in some places. That's why I run my business under my own name. The added benefit is that, depending on how things go at the end of the year, I can decide whether to file taxes as a business or as a hobby.
Also, I would look a little more into the use of the title "Ltd." Unless you incorporate the business, you may not be legally allowed to use that. I could be wrong, I'm not a lawyer. But it bears looking into it to avoid troubles down the line.
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