Suitable methodology to assign job titles to categories
This is regular text classification, but with very little text (only the job title). You could start with a simple one-hot encoding over the words in the job title, then apply your favourite algorithm (e.g. Naive Bayes, Decision Trees, etc). It will probably work better with some form of normalization of the words (at least using the lemma in order to mach variants of the same word).
Word embeddings are probably a good choice too, but my guess is that this would help only if you have a quite high amount of examples.