Sorting out the present perfect, participial phrases, gerund nouns and gerund phrases.
The present perfect is this:
A - He has taught for many years.
B - We have learned how to read Hindi.
The present perfect is have + a past participle (third person s or es) as can be seen above and below:
- have been
- have seen
- have walked.
You can see that you cannot add ing to those two sentences (A and B).
Now, let's look at the type of verbal phrase you are trying to use based on A and B:
A - Having taught for many years, he decided to leave the profession.
B - Having learned to read Hindi, we were now able to read many new authors.
Those are called participial phrasea.
Participial Phrases are present participles or past participles and any modifiers, objects, or complements. Participial phrases contain
verbs which act as adjectives in a sentence.
Your examples are similar to those in that they use participial phrases:
Having been tired of trying, he wants to give up. [See corrections below]
Having become tired of trying, he wanted to give up. [past participial phrase]
Being tired of trying, he wants to give up. [present participial phrase]
Please note: We would often use: as he became tired and as he is tired, as those participial phrases are somewhat heavy, though they can be very useful at times.
Finally, your question is really about transforming a present perfect into a participial phrase and not a noun.
In: /I like his way of teaching./, teaching is a noun, called a noun gerund or gerund. Of course, it is also a verb: I am not teaching this afternoon.
You can form nouns from any verb by adding ing, and sometimes you have to double the consonant (stop, stopping) or drop a vowel (leave, leaving). However, that was not the actual issue brought up in the question's examples.
Finally, there are gerund phrases that can be used as the subject of a sentence:
- Having eczema is no fun.
- Having been a thief was his burden to bear.
A gerund phrase is a phrase consisting of a gerund and any modifiers
or objects associated with it. A gerund is a noun made from a verb
root plus ing (a present participle). A whole gerund phrase functions
in a sentence just like a noun, and can act as a subject, an object,
or a predicate nominative.
Bear in mind: some gerunds (get, getting, drop, dropping, leave, leaving, please, pleasing) call for doubling the final consonant or dropping a final vowel before the ing.