I reviewed several texts and research articles. In my limited search, I found the term "ansa cervicalis" - without the "superficial". Could you provide a reference or example where the term is said to no longer be in use? Is it noted in Nomina Anatomica?
On a side note, I found this discussion based on a twitter debate - https://litfl.com/de-eponymising-anatomical-terminology/ - that I though was interesting regarding the removal of eponyms from anatomical literature. It is an interesting read.
In Terminologia Anatomica (which replaced Nomina) ansa cervicalis has superior and inferior limbs (roots or radices). Neither ansa cervicalis profunda or superficialis are listed, but both are in use especially in the European literature. I don't think that these correspond to the externus and internus modifiers that one sometimes encounters (e.g. Shvedavchenko, A.I., Oganesyan, M.V., Hammer, C.M., Paulsen, F. and Bakhmet, A.A., 2019. Ansa cervicalis—A new classification approach. Annals of Anatomy-Anatomischer Anzeiger, 222, pp.55-60.) The profunda may correspond to the ansa cervicalis proper and the superficialis is not part of it strictly speaking. Please correct me if I'm mistaken.