Can we end a sentence with 'Past participle'?
For example:
- Tell me more about the sentence you've given.
- What was the name of the food you've eaten?

Also,
Is it correct if we use the word 'gave' instead of 'given'?
- Tell me more about the sentence you gave.
- What was the name of the food you ate?

Which one sounds more natural to your ears?

Also,
Should we use the verb 'Is' instead of 'Was'?
- What is the name of the food you ate?

Question

Can we end a sentence with 'Past participle'?
For example:
- Tell me more about the sentence you've given.
- What was the name of the food you've eaten?

Also,
Is it correct if we use the word 'gave' instead of 'given'?
- Tell me more about the sentence you gave.
- What was the name of the food you ate?

Which one sounds more natural to your ears?

Also,
Should we use the verb 'Is' instead of 'Was'?
- What is the name of the food you ate?

Answer

Those sentences are all fine and natural.

Answer

The difference between the two sentences is just time. Past and present perfect. You can use both, you should choose time.

Food name was... is incorrect I think.