The SEC is not a registry of all businesses in the US. The SEC concerns itself with business that sell shares to the public; this would not cover (for example) a single-member LLC that a software developer might use.
In the US, businesses are chartered and registered by the states, not the Federal government. There is no Federal equivalent to the UK's Companies House.
In the US, businesses are chartered and registered by the states, not the Federal government. There is no Federal equivalent to the UK's Companies House.