Can't delete I think. You could of course just put all sorts of deflective stuff in your profile to make it totally impossible to guess it was you and then just leave the profile dormant.
Problem of say deleting a facebook profile, as in totally deleting it, is that all your FB posts ever made on any FB forum will disappear forever too -- including your comments on your grandkid's this and that photo etc. But at least they do give you that particular nuclear button to use to tidy up after yourself.
Here is a guy who went to delete his FB account, watch what happens:
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