Your employer can't take instructions from you personally, to change the amount of tax they deduct under PAYE. If there is a mistake you have to get HMRC to send your employer a new tax code.
The tax codes should ensure that all your personal allowance is "used" by your employer(s) when calculating how much tax to deduct - unless your total income is less than the allowance, of course.
You may get a PAYE Coding Notice from HMRC each year, which tells you how your tax-free allowance is split between your various sources of income.
If you only have one employer, you may not get a Coding Notice every year, but you should get one if your circumstances change (e.g. if you change jobs). The "annual" statements are sent out before the start of each new tax year, i.e. round about now - I got mine through the post a couple of days ago.
If you don't have a Coding Notice, you can ask HMRC for one. Contact details are here: https://www.gov.uk/government/organisations/hm-revenue-customs/contact/income-tax-enquiries-for-individuals-pensioners-and-employees.
Note: if you have just started your first job, you will probably have an "emergency" tax code which does not take account of your personal allowance. When your employers get the correct code from HMRC, your deductions up to the end of the tax year will be reduced, so that you will have paid the correct amount of tax by the end of the tax year. An emergency code would be shown on your payslip as a number followed by the letter E.