From Tolkien Gateway

I'm of the opinion that we should try to keep this being a linguistic article - it's hard to conceptually separate from Taniquetil, which in at least in The Silmarillion seems to be the main name of the mountain.--Morgan 20:43, 4 June 2011 (UTC)

In the first place, Ardalambion's wordlist says Taniquetil is the name of the peak, while Oiolosse is the name of the mountain. It seems to be reflected by the names. I tried to make such separation in the articles. Sage 21:49, 4 June 2011 (UTC)

I don't think it is possible to uphold such a separation, i.e., a clear distinction between Taniquetil and Oiolossë. If Tolkien envisioned Taniquetil to be the name of only the peak, and Oiolossë to be the name of the mountain as such, we wouldn't see statements such as these in The Silmarillion:

"For [Manwë's] throne was set in majesty upon the pinnacle of Taniquetil, the highest of the mountains of the world, standing upon the margin of the sea."
"And above all the mountains of the Pelóri was that height upon whose summit Manwë set his throne. Taniquetil the Elves name that holy mountain, and Oiolossë Everlasting Whiteness, and Elerrína Crowned with Stars, and many names beside; but the Sindar spoke of it in their later tongue as Amon Uilos."

I guess Helge Fauskanger bases his theory on a note by Christopher Tolkien in the Index to The Silmarillion, which says: "... according to the Valaquenta [Oiolossë] was the 'uttermost tower of Taniquetil'", in conjunction with the linguistic argument you mention (which is, that Taniquetil contains a stem meaning "peak"). On the other hand, CT also says (in the same index entry): "[Oiolossë is] the most common name among the Eldar for Taniquetil". The passage to which CT is referring reads as follows:

"[The halls of Manwë and Varda] are above the everlasting snow, upon Oiolossë, the uttermost tower of Taniquetil, tallest of all the mountains upon Earth."

In my opinion this sole quote, which in itself isn't easy to interpret, is too scant evidence to make a clear-cut distinction. However, I wouldn't mind a mention in any of the articles (either the Oiolossë or the Taniquetil article) of Helge's theory (if it's clear that it's a theory).--Morgan 15:34, 5 June 2011 (UTC)
I would say it's pretty clear from both the Index and the former quote that Oiolossë and Taniquetil are one and the same. Furthermore, the latter quote doesn't actually have to be interpreted as "the uttermost tower of Taniquetil is Oiolossë"; it could be read that "the halls of Manwë and Varda are on Oiolosse tallest of all the mountains upon the Earth and on the uttermost tower of Taniquetil". --Mith (Talk/Contribs/Edits) 16:17, 5 June 2011 (UTC)