I am afraid not of catching commas in spoken English

I am afraid not of catching commas in spoken English and I am wondering if I must notice commas in spoken English and if there is always meaning difference to distinguish or the difference is too small to notice, so I can ignore the difference?

ex)

A U.S. official, who asked not to be named, said ....

This is about one official. We don't know anything about him except that he asked not to be named. This detail is given as an aside - it is not an important part of the message.

A U.S. official who asked not to be named said ...

This is about one specific official. He is identified as the one who did not wish to be named. This identification is an important part of the message.

I am not sure that I can hear the commas in spoken English and I would understand the first one with commas as the second one without commas in spoken English although there are commas like the first one, and then, is it a big problem?

I feel like understanding the one with commas or without commas does not make big trouble sometimes.

What do you native English speakers think? Thank you so much and I am sorry about asking the same questions.