Learn English – “a company which name is” or “there is a company whose name is”

I think you are making it too complicated!

"Of whom/whose" would normally refer to a person, not a thing. The book called Manwatching was written by Jellison. No need for of whom or by whom:

If you are writing about a person, again there are much simpler ways to express the same thing. All you need to say is:

Michael Patterson is the manager.

Or maybe:

The manager's name is Michael Patterson.

Now the two example sentences you give are, I suppose, correct. You might see something like

After a long manhunt, we have finally apprehended the suspect, the name of whom is Michael Patterson.

So grammatically your examples are correct, but it is considered poor style to separate a subject from the verb by too many words. Note that in the "manhunt" example the clause is moved to the end, to avoid separating the subject from the verb.

Of the two patterns you suggest

The man, whose name was Michael, was the manager.

Is better. I've set off the middle clause with commas to help readers.

The students, whose names I don't remember, were all very smart.

Is better than using "of whom". Even so, I would still prefer:

The students were all very smart, but I don't remember their names.

English does allow for sentences to be expanded by inserting relative clauses in them. But its usually not a good style. You might look at the old nursery rhyme "The house that Jack built" to see what happens if you take this process too far.

"... the person ..."

If it said "a person" it would imply that there may be more than one person with the same signature and photograph and that one of them is an employee. This is probably the exact opposite of what you what to say on an ID card.