Can I claim a 1098E of a parent plus loan which is under my father's name but I make all the payments?

Yes, your parents may claim the loan interest deduction on a Parent Plus loan : The  student loan interest deduction reported on form 1098-E is an adjustment to income up to $2,500 under income limitation - If you're married filing separately, or for 2020 if your modified adjusted gross income, or MAGI, is $85,000 or more if filing single or $170,000 if married filing jointly, you can't deduct any student loan interest. Your MAGI is essentially your adjusted gross income (AGI) with certain deductions added back in.

No.  In order the claim the deduction you must actually pay it and be legally responsible for paying it.  So, unless you are a co-signer, only your father can deduct it.  He cannot deduct it, even though he didn't pay it under the theory that you paying is actually a gift to him, and he therefore paid it with his money.