If a distribution has been given, after exiting a job, with the penalty and taxes already taken out, do the final amount still need to be filed on tax return?

I assume you are asking about a 401K or something.  You will get a 1099R for it.  Yes you have to enter it.  Even if you roll it over.  And if you roll over the remaining amount the taxes and penalty will still be a distribution unless you add them back into the rollover from your own money.

You didn’t actually pay the tax or the 10% penalty (you pay a 10% early withdrawal penalty if you are under 59 ½). You had taxes withheld like from your paycheck. You still have to enter the whole gross amount (before taxes were withheld) with your other income to figure out the total tax (and it may put you into a higher tax bracket) and then the withholding is subtracted from the total tax to figure your refund or tax due. The Gross amount shows up on 1040 line 4a or 5a and the taxable amount on 4b/5b. The withholding will show up on 1040 line 25b.

It has to break out and show the 10% penalty separately on your return (schedule 2 line 8 which goes to 1040 line 23). Then you get credit for all the withholding taken out on 1040 line 25b.