That website is beyond inaccurate and thus useless. I recommend avoiding it.
Now... Firstly, there is no "Elvish". Or rather, there are multiple languages and "Elvish" is rather an umbrella term for all. The most important ones are Quenya and Sindarin. Quenya is like what Latin is to us, an old language of science and ceremony. Sindarin is like English, a common tongue for (basically) all Elves.
Forming names in Quenya is often as simple as combining two words (though not always). But more often than not, name formation in Sindarin requires expert level knowledge on the historical phonetic development rules of the language, as I demonstrated here. So the only "good way", in my opinion, is to consult experts.
In other words, simply list the meanings (not Elvish words) that you would like for the name, and I would form the name for you.