Usage of commas within sentences

I must have asked the same question before and I think that I got answers from teachers here but I forgot what they were so I searched for it. However, I failed to find it so I am asking this again. I am sorry for taking your time.

My question is about usage of commas and I was wondering if it does not make meaning difference with or without commas here.

"Military officers said today that the two staff sergeants, only identified by their family names Lee and Cho, collapsed late Tuesday."

I think that without the commas like "Military officers said today that the two staff sergeants only identified by their family names Lee and Cho collapsed late Tuesday." is also possible and there is no meaning difference between either one.

What do you native English speakers think? Thank you so much as usual in advance.