What is this gourd-like vegetable?
Going by your guesses, I found the following names on Wikipedia (all for the same plant): sponge gourd, Egyptian cucumber, Vietnamese luffa, dishrag gourd, rag gourd, vegetable-sponge or smooth luffa. Its Latin names are Cucurbita luffa, Luffa cylindrica, Luffa aegyptica, Luffa aegyptiaca, Luffa pentandra, Momordica cylindrica. or Momordica luffa.

I am not completely sure if the plant in the photo is the plant on the Wikipedia page. However, the Wiki has a translations in many different languages, so perhaps you can look for one in a language in which you know the plant's name?

Edit: Given your updated tag of Indian, I should point out there are Wikipedia pages for the vegetable I linked to in Hindi, Marathi and Tamil as well as 28 more languages.