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Usually it's a job for a mapping, for example with something like:
[B]: mapping load Title as Lookup, Profession as Return; SELECT Title, Profession FROM "public"."B";
[A]: SELECT Name, Departement, Profession, applymap('B', Profession, 'Default') as New FROM "public"."A";
But in your case you will need a second column containing the return-values because only with one column Title = Profession or it does not match. I assume here that your description is just not complete.
Thinkable are also approaches which search for sub-strings but in this case you will need a defined logic which sub-strings will lead to a valid matching.