The term you're looking for is "Fictitious Business Name," or "Trade Name."
Generally, the legal ramifications are a requirement to register the name and pay a small fee. In Santa Clara it costs $40 to register a fictitious business name with the county and the registration is good for five years: https://www.sccgov.org/sites/rec/Fictitious%20Business%20Nam...
It's really not a big deal.