A name means nothing. Don’t know what country you are in, (asume USA I am in the UK) But most capitalist societies expect TAX to be paid on any profits, regardless of a name. A name means little to the tax people.
Keep records of income and outgoings. If no profit, no tax.
sales minus expenses = taxable profit.
If you are in the USA, this discussion below might help too. But I advise you to read it all.
I have a ‘name’ for my snake business ‘Ascended Royals’ i am also in the beginning, so my expenses well outweigh sales. So no tax worries. (as long as I have records to prove that)
My other main business does make a profit, name or not, so the government wants plenty of tax for that.