[ceity]

Are there other ways to name these compounds (photo attached)?

[Dan]

Yes, but there is only one IUPAC name.

You could call the first one: 6-(3-carboxyphenyl)hexan-2-one

People would understand what you meant, and could translate it to the right structure, but it is not correct in the sense that it doesn't follow IUPAC conventions (the priorities are incorrectly ordered).

It's basically a language - an analogy would be the way Yoda speaks in Star Wars - you can understand what he's saying but it sounds strange because his grammar is not very good.