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For example, let’s say I’m writing an article about cooking tips and in the body content I link to another article with the title “How to Cook Chicken” and I want the text link to have the same anchor text.
I want the ability for this anchor text to change automatically in each article that it is placed in if I instead change the title to “Cooking Chicken – How To”
Is there a basic function in WordPress that makes this possible?

Not built in, no. That may change in the future, but it is not built into the current version.