Bsrhrki

There are those among us who prefer soda to coffee, namely Robert and
Mathilda.

Does "namely" imply there isn't anyone else other than Robert and Mathilda who prefers soda to coffee, or does it mean there might be others aside them.

“Namely” is similar to the phrase “to name names”. It can be used to introduce the only people of a given group (known to the speaker/writer) for whom the previous statement is true. Or, I think it can be used to single out people to emphasize that the previous statement applies to them. Robert and Mathilda might be the only people present who the speaker knows to prefer soda to coffee. They could also be two people that the speaker wishes to tease or otherwise draw attention to for not liking coffee, even if there might be others present who also prefer soda.

Another way to understand how the adverb namely is used would be to substitute it with the adverb specifically:

There are those among us who prefer soda to coffee, specifically, Robert and Mathilda.

This implies that Robert and Mathilda are the only people in the group who prefer soda to coffee. In other words, there are people in the group who prefer soda to coffee. But if you want to be more specific, their names would be Robert and Mathilda. When the statement is posed this way, it is obvious that there are no other people in the group who prefer soda to coffee.

to be specific, by the way, is listed as one of the definitions of namely in the Oxford Dictionary:

That is to say; to be specific (used to introduce detailed information or a specific example)

As was aptly mentioned in one of the answers, namely basically means to name names. You say namely and then you list a bunch of names that you think are linked to the situation you're talking about. This is very similar to how you would typically use the adverb specifically. You would make a statement and then you would say specifically to give a list of specific names that you think are directly connected to the situation.

The adverb namely in the sentence means "that's to say". You use the namely to say the names of the people or things you are referring to, For example:

Three students were mentioned, namely John, Sara and Sylvia (Longman).