I’m curious, being a county does that also imply that a Count of LA exists? And the same for each county in the USA?

The counties are administrative and there are bureaucrats who lead the county, but they are not titled, noble Counts and Countesses.

In Sweden, we also have administrative regions translated as counties, which are lead by someone I'd directly translate as "county chief" (as in "chief over this tribe") but they're anonymous bureaucrats a normal person wouldn't know about. (The common translation is the less exciting "governor".)

Not even true for the UK, which does have geographic peerages but they're not really linked to the county boundaries any more.

For some reason, the UK doesn't issue the title of "count", only "viscount". "Marquis" is linked etymologically to "marches", an old type of land allocation boundaries, but again not in practice.

The UK version of "count" is "earl".

No. To quote Hank Hill, we fought an entire war with England over that.

Not that rare in California. Off the top of my head: Sonoma, Napa, Mendocino, Santa Clara, San Mateo, Santa Cruz, Monterey, San Diego, San Bernardino, and Alameda counties all have cities of the same name. Seems rare in most other states though.

It is rare in most states, I believe. It is very common in South Carolina (see https://en.wikipedia.org/wiki/List_of_counties_in_South_Caro...), which has counties named things like "Greenville" and "Spartanburg" after their largest cities - it feels to me like those should be "Green" and "Spartan". And then there are states like Georgia where there are counties, and cities with the same name that are in different counties, because the county-namers and the city-namers were pulling their names from the same pool of well-known people but weren't talking to each other.

Also, in California: San Luis Obispo, Riverside, Sacramento, Fresno, Santa Barbara.

Don’t forget Orange!

SF’s city and county are actually both the same land. In the other cases, the counties are usually larger (at least in California).

SF city and county are actually the same legal entity, not just the same land. It's officially called the City and County of San Francisco, and it's just as unusual as it sounds. The mayor also has the powers of a county executive with both a sheriff's department (county police to run the jails) and police department (city law enforcement) reporting to him; the city government runs elections like other counties; the Board of Supervisors - which is the typical county legislative structure - also serves as city council. (Denver, Colorado works the same way, I think.)

Philadelphia is another example.