It is not always être, it is not always a profession, it is not always one verb, and it is not always one noun.
- Quand j'étais enfant.
- Ils sont cousins.
- Il demeure Président du Conseil d'administration.
- Marc et Marie sont frère et soeur.
- Je veux être ingénieur.
- On est devenus architectes.
What are these verbs? - Stative, Linking, or Copulative?
They are stative verbs, specifically linking verbs, and include the copulas. The majority of the internet (in two languages) seems to confuse these three terms and use them interchangeably. A stative verb (verbe d'état) expresses a state of being, not an action. The verbs include "to think, feel, see, have, smell, depend, penser, sembler, dépendre de, étonner etc). Some stative verbs link attributes to the subject, hence they are called linking verbs (verbes attributifs). These specific stative verbs must have a predicate adjective or nominative after the verb (get, turn, grow, avoir l'air, passer pour, s'appeler, etc). The copulas (copules) or copulative verbs (verbes copulatifs), are mores specific and have no other extra purpose than to link the P.A. or P.N. to the subject. English and French only have one: (to be, être). Other languages like Russian and Japanese simply leave them out, while languages like Spanish and Italian (ser vs estar) have two in order to denote the permanence of the predicate's arguments. You will hear linking verbs sometimes called "semi-copulas", but I digress.
Okay... so what about the noun?
It is used to talk about professions, but not job descriptions. It is used to talk about religions, but usually these words are already adjectives. It it used to talk about family members, but mainly in the plural (frères et soeurs, cousins, parents, etc), or for a person who cannot have a job (enfant / gamin). This seems to describe the function in the family, or more specifically the name of the role in the family, in a group, in a life, or in a job. Not all linking verbs can be used with a Predicate Nominative, specifically as a role, so we make a list.
My proposed formula:
[Verb Phrase ending with: être, (re)devenir, (re)nommer, rester, demeurer, (ré)élire]
[Noun Phrase that describes the name of a person's role being used as an adjective]
Or the condensed version:
[sujet] + [verbe attributif] + [rôle]