I don't see that. Great man tradition and generations i have a different opinion on, especially if the remains of a tribe got adopted into another tribe already, theres no easy way back once it is done.
Adoption would only work if:
- all the House of Beor orphans get adopted in the families of other Houses,
- all the mothers with little boys remarried and their new husbands adopted all the House of Beor boys replacing their father's names
or
- if their fathers-in-law adopted them after they grow up and marry at the time of their marriage to the daughters from other Houses.
It would not take place at all if a House of Beor boy would mary a House of Beor girl.
And not all older House of Beor people have yet died off, those are too old to be adopted anyway.
And what about middle aged unmarried people? - Those remain "unadopted" also.
A "tribal adoption" - without a new father - is always done to an adult person in some very extraordinary cicumstances.
Once adopted all the successive offsping of the adoptee belong to the new tribe - but not necessay older childen born before, who are of age already.
Adoptions always concern an individuum and never a cohort.
What could be done is that the House of Beor people explicitly reject Dior as "an
unnatural freak" having
not been born of a "
real mortal woman" - understood as a woman whose maternal lineage goes back to some legendary "Mothers of Men" - (not being a "Daughter of Eve" - using Lewis' terms).
Then, such rejected and offended, he would accept Thingol's legacy. But still his obligation to try his fathers people first when he comes of age is clear and cannot be dismissed (at that time Thingol is still in office and the House of Beor is leaderless - Beren is forbidden to retun to them as a resurrected being - but Dior is available). He has not been raised in Doriath either - it is equally foreign to him.
Finrod's sucessors too as he has no direct heirs.Then all obligations died with him.
Still there are Finrod's companions who still might have relatives around. And Finrod's nephew and grand-nephew are a succesors kin enough to inherit this obligaton. Actually this might be the reason why Elrond does
serve under Gil-Galad.
As for 'Eluchil' - obviously, this is not a surname, because Elves don't use surnames. The sobriquet means 'Heir of Thingol,' and is a reminder that he has the right to the throne of Doriath. Thingol died, leaving behind no son. His daughter Lúthien has shown no interest in ruling, and no longer lives in Doriath. So, inheritance passing through the distaff line is not that unusual, though we have established that Elves have rather unique views on inheritance, not necessarily expecting to need an heir. Dior, on the other hand does expect this - he names his sons Eluréd (Heir of Thingol) and Elurín (Remembrance of Thingol), making their roles as suitable future kings clear in their names. And, naturally, it is in honor of Thingol, which...brings us back to this season.
Elves do use patronyms. And Dior's sobriquet was "the Fair" as far I do remember? Dior indeed honours Elu a lot, as such there must be something about Elu to be honoured - excactly my point. One does not name himself and own's children after a total jerk even if one inherits the throne from him. Especially as Dior named both boys this way when Thingol was still alive and well and nobody (except maybe Melian) thought his thone will ever be inherited. Dior devotion to his grandfather predates his death. When have they met, actually?