I have been having a decent paying job since 10/31/2023 and my tax dependent just bought a vehicle in their name. is their any chance i can update this information now?

there's no way to enter 2023 info in the 2022 file unless you want a potential mess on your hands when you go to do 2023. if you will be an employee, the vehicle will have no tax benefit (maybe state). you say they purchased it in their name. whose name is on the title? if it's theirs you don't own it so thus if even if an independent contractor you would not be entitled to depreciation.   and if they put your name on the title, in effect making a gift to you most likely they need to file a gift tax return.  

Did you file your 2022 tax return?   None of that info goes on your 2023 return next year.  The 2023 online version won't open until late November or early December.  The Desktop CD/Download program usually comes out in early November.  

Q. Is their any chance I can update this information now?

A. No. That can't be done. 

You'll have to wait until the 2023 software is available.  Furthermore, you dependent's vehicle ownership is irrelevant (on the federal return) and there is nowhere to enter that. 

For more specific advice, please explain what it is you are trying to accomplish. If this is a state issue, identify the state.  

Your "best friend and father of your son" can't also be your tax dependent unless you provide more than half their financial support, and they live in your home all year, and their taxable income is less than $4700.

(Your son can be your dependent, of course.  If you live together unmarried with the father, then your son can be the dependent of either yourself or the father, but not both.)

Your partner might still be your tax dependent for 2023 if they still meet all 3 tests, even though they bought a car.  If they don't meet the tests, they are not your tax dependent when you prepare your 2023 tax return.  If you claimed 2 dependents on your W-4 when you started the job, you could give your job an updated W-4 that only claims 1 dependent (your son, if you plan to claim him).  

Note that an adult dependent is an "other" dependent that gets you a $500 tax credit, so the effect of not claiming your partner for 2023 would be a $500 increase in your taxed owed or a $500 reduction in the refund you expect.  Changing your withholding would lessen the effect of the change, with fewer dependents means having more tax withheld from each paycheck.