regexprep(name, '\d[0-9_]+\d', '')
This expression makes the guess that underscores should only be removed if there are digits on both sides of them, so for example in 1234_abcd this would become _abcd . This guess is supported by the wording of the Question.
On the other hand, the expression above has the weakness that multiple underscores together will be deleted if the group is between numbers. This is not supported by the wording of the Question. I think that perhaps the below would work to fix that:
regexprep(name, '\d+(?:_(?=\d))?', '')