While it may have an extensive legal jurisprudence, this issue is total separate. The rights protected in the constitution relate to the state.
For example, we have a right to assemble and the state can not deny that. However, a private entity can prevent us from assembling on their property.
In the same way we have a right to anonymous speech and the state can not deny that. However, a private entity (Quora) can prevent us from making anonymous speech on their website.
The reason for this is obvious, would you want newspapers to have to allow the rantings of a raving lunatic if he used a pseudonym to sign it because it can't prevent anonymous speech?
For example, we have a right to assemble and the state can not deny that. However, a private entity can prevent us from assembling on their property.
In the same way we have a right to anonymous speech and the state can not deny that. However, a private entity (Quora) can prevent us from making anonymous speech on their website.
The reason for this is obvious, would you want newspapers to have to allow the rantings of a raving lunatic if he used a pseudonym to sign it because it can't prevent anonymous speech?