In this sentence
你叫我马丁好了。
what's the role of 好了?
I understand this sentence as "You can call me 马丁."
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你叫我马丁好了。
what's the role of 好了?
I understand this sentence as "You can call me 马丁."
By using this word, you are reminding the listener that "you don't have to worry about [something]; just ignore it; don't be so polite; don't speak so formally."
In your case, the speaker wants to express that "It's OK to call me 马丁. Just call me 马丁. You don't have to be polite and call me something like 马先生 (Mr. 马). Take it easy."
In Chinese, the particle 好了 is used to mean "OK".
So in the sentence
你叫我马丁好了。
this would be translated as "You can call me Martin, OK."
好了 is also used to suggest something where you are not expecting a response:
现在我带你去看他好了。 = I'll take you to see him now.
In this case, the person could still refuse or suggest now is not the right time. But by using the 好了, the speaker is suggesting that the other party is likely to go ahead with the suggestion.
Contrast this with a sentence where 好吧 is used, which is more offering a suggestion:
我们现在去看他好吧? = Let's go and see him now, OK? or How about we go and see him now?
Also note that 好了 can be used in another context to indicate completion, e.g.:
你吃好了没有? = Have you finished eating?
It has no special meaning. It just establishes a tone similar to 就...吧.
“你叫我马丁好了” equals “你就叫我马丁吧”.
If you really want to find a homologous word in English, it's "can just", in my opinion.
“你叫我马丁好了” means "You can just call me Martin".
“我带你进去好了” means "I can just bring you in".
In this sentence
你叫我马丁好了。
what's the role of 好了?
I understand this sentence as "You can call me Martin" or "Ma Ding".
It can just be a verbal tic (embolalia) like 'right?' or 'y'know?' in a situation where the speaker believes the listener already knows what he's saying. It's basically the same thing as
You can call me Martin, y'know?
when the question is rhetorical and the speaker thinks the listener is going to agree. (In places where agreement is uncertain or not expected, you'd use 好吧—OK? alright?—instead.)
Technically, it's saying that the preceding statement is 'good' or 'fine'. We'd usually express it in a different order in English:
It's fine if you call me Martin.
It's OK for you to call me Martin.
了 at the end of the sentence marks it as a factual situation.
That is:
So what is the difference between 2 and 3? Why did someone thought that he must put additional stress (in the form of 了) to the sentence 3?
Clearly the speaker tries to convey some additional meaning to the sentence 3. I think he wanted to stress that It is not just OK, but it should be OK from now on or He is just tired that before the speach it was not OK.