Bash
for file in prefix*; do mv "$file" "${file#prefix}"; done;
The for loop iterates over all files with the prefix. The do removes from all those files iterated over the prefix.
Here is an example to remove "bla_" form the following files:
bla_1.txt
bla_2.txt
bla_3.txt
blub.txt
Command
for file in bla_*; do mv "$file" "${file#bla_}";done;
Result in file system:
1.txt
2.txt
3.txt
blub.txt