Have Wilkinson die on the Erie instead of Wayne and a general more favorable to the idea of calling the federal force a legion replace him: legion potentially saved. You just really need to convince Jefferson down the road that a token federal force is practical (it would be outnumbered by state regiments anyway). The core problem: I don't know one, and besides Jefferson I feel Jackson and the "era of good feelings" presidents might take issue with the idea of a permanent force as well, so you'll need fairly eloquent commanders of it for the next 25-ish years.
Reorganize the legions into a dual division/regiment system, as the french used. Voilà, the First sub-legion restored to 1st regiment.
Have more formalized state militias required to maintain a regular regiment of foot, maybe a squadron of horse and an artillery battery too (a sub-legion, which was basically a mixed brigade, replacing the fourth infantry battalion of the typical european square brigade by its own cavalry: that's basically a ww1 triangular formation, which the US had stopped using in the meantime, but war in the lightly populated americas could potentially justify the maintenance of such an organization, it would also give a better cavalry core in the ACW = better recon, better communications, more efficient staff work on both sides); put this as a guideline for statehood (capability to raise such) in addition to the unofficial guideline of roughly 80.000 people. It probably doesn't survive all the way to today, but it might survive longer.
The Legion might not survive except maybe as a ceremonial unit, the State Regiments would probably be federalized during the ACW, a few years later for the southern ones, and so change numerotation, but by then they'd have been established for about a century. Have the legion form the core of the union army if the ACW unfolds as OTL, at this point it might have enough prestige that it remains the presidential guard instead of the marines (the navy would probably get their guard marines regiment anyway sometime in the 20th century).
The French might help repopularize the term, since they did have a Vistula Legion that was the polish forces directly under french command, along with the Legion Belge (Netherlands), Legion Irlandaise (Irish émigrés), Légion Noire (from freed blacks during the 1st republic), it seems to have been a fancy term for a unit larger than a division but smaller than a "full" corps, or foreign troops.
Okay I stop editting, promise (I lied)
- if the regiments remain structured with a grenadier company to each battalion, the combined grenadiers (as was european practice but I admit to have no idea how the US army worked at that time besides the great lines) can even be your First Battalion on the field, for added adherence to classical forms.