Question about transferring luggage between International and Domestic US flights, NRT to LAX then to PHX

Hi, I'm flying from Narita-Tokyo to LAX in Los Angeles next month, but I have another flight afterward from LAX to PHX-Phoenix in the US, but I booked the flights separately because I wasn't certain what city I was going to after landing in the US when I purchased the original Tokyo-LAX ticket
Will they transfer my checked luggage between the international & domestic flights automatically, do I have to request that, or will they give me my checked bag to transfer it myself?
Sorry, no idea how that works, just don't want to risk leaving my checked luggage behind in LAX

Thank you

Oh and the flight from Tokyo to LAX is with ZipAir, but the flight from LAX to PHX is with Southwest Airlines, don't know if that changes anything