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I have no idea if it has a name. But since traditional priests (including bishops) are not legislators in the Church, and have no proper spiritual authority to bind the faithful to anything, it's the only solution available. However priestly groups want to organize their investigations into marriages is their own business, but one thing they literally cannot do is set up tribunals-- if by tribunal we mean an authoritative body with sufficient power to compel lay behavior and conduct.

Hasn't the SSPX agreed to have marriages co-validated by the NO? Would then, the NO have jurisdiction over SSPX annulment proceedings? I think so. Why would they venture off into this territory when they already have an overseer?

IMO, unless it's a clear cut-and-dry canonical case that a prior marriage was invalid, i.e., baptized Catholics getting "married" in front of a Justice of the Peace, in this time of Crisis, all marriages must be assumed valid, and people have to live with the situation.  Given how very few annulments were granted prior to Vatican II, this accurately reflects the mind of the Church.  Anything that involves "intention" or "psychology" or any of that nonsense ... needs to be ignored and the marriage assumed valid.

Supplied jurisdiction does not cover discernment regarding the validity or invalidity of marriages, and the NO either do not have the authority (if you've an SV) or else simply cannot be trusted to provide the proper discernment.

So, we need to recall that the Church does not annul marriages, but simply renders a verdict that binds consciences.  Who has the authority to do that?  Traditional Catholics don't, and the NO are so reckless that their opinion is smiply not trustworthy.  That's why SSPX is getting into this "vow" business, where the couple bind their own consciences ... but that's also problematic because in reality the couple cannot even bind their own consciences.  To think that a couple can bind their own consciences based on some discernment process is one step away from Amoris Laetitia.

Conversely, however, if a couple go get a decree of nullity from the NO and they believe that the NO have the jurisdiction to bind consciences, I also hold that Trad Catholic clergy to not have the right to refuse them the Sacraments ... as that too entails binding consciences, an authority that they lack.