Need a Sindarin Expert

I just got here and I 've been thinking about getting myself a Sindarin name.However it's been haunting me for days for I hardly know the rules of this…naming stuff (Thank God I found this page)

The meanings I'd like to have for my name is "glimmering fountain", which I got " gael /celeth"in Sindarin, at first I just simply put them together as "gaelceleth"(well it sounds good to me), but my friend told me that it's definitely not gonna work, so I really need your help here, hope that you can form a suitable name for me.It's ok to change "glimmering" into another similar word if there's a better option,but I'd like to keep "fountain"(one of my favorite words)

I'd be really appreciated if anyone can help me on this. Counting on you guys!

Note that celeth is rather the Noldorin (read: draft-Sindarin) word for a stream or brook, literally meaning "a flowing." I'd accept it as valid for that sense in Tolkien's later conception, but I'll defer to more Sindarin-focused experts. If you're after the meaning "fountain" as a spring or source of water, I'd suggest eithel.

Thank you so much!!!
In that case it'll be "gaeleithel"Is that ok for a name? Well actually I'm still confused about the naming rules, I did notice a word " Mitheithel ", but when it comes to names, should I shorten the word or add a suffix or what?

[...] my friend told me that it's definitely not gonna work [...]

Your friend sounds wise. Compounding (or name formation) is one of the most complex subjects in Sindarin, despite being rather straightforward in many other languages. It is so complex, in fact, that it requires one to be familiar with the historical phonetic development rules between the Primitive Quenderin (> Common Eldarin > Ancient Telerin > Old Sindarin >) and Sindarin stages. Here is an example that I had written some time ago.

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Well actually I'm still confused about the naming rules

If you are referring to this comment from me, the basic rule is that neither "glimmering" nor "fountain" can work as names by themselves (no single adjective or noun would), but their combination would indeed work. As for the word choices, I agree with Röandil that eithel is the right word for "fountain". And regarding "glimmering", I would rather pick another word, because the etymology of that one is questionable. But other attested alternatives are also somewhat unfitting (either due to etymology or connotation), so I would use *tend (cf. Q. tinda) which can mean "gleaming, glinting, glittering, glimmering, shimmering, twinkling, sparkling" (Tolkien used them interchangeably in his translations to English). Combining that with eithel would yield either (older) Tinneithel or (newer) Tenneithel.

Though if celeth is one of your favorite words based on sound, and you don't mind the shift in meaning from "fountain" to "stream," that could still be an option.

El, would those produce †Tingeleth and Tengeleth?

Wow that really helped,thanks a million!!!