Hi there,
I run my business from home, microblading and other brow treatments. I do not have a problem getting clients. I trained in microblading about 3 years ago when it wasn't so popular so it may depend on how much competition you have around you.
I have a website which states that my treatment room is based at home and has been checked and licensed by my local council - I then provide a link to the council website as proof before they actually book in. I also provide information on the level of qualifications I have, who I trained with and a photo of my set up. As long as you keep it really professional you shouldn't have any issues. If you're solely microblading I would keep it quite clinical looking.
Because of who I trained with my prices are higher than the average salon and I still don't have issues with gaining clients. I definitely wouldn't sell yourself short as you will regret it in the long run and attract the wrong type of clientele (in my experience in the early days). A lot of people nowadays see cheap prices as a cheap treatment.
Good luck!