[<common-part>-<random-text-a>, <common-part>-<random-text-b>]

[<random-text-a>, <random-text-b>]

import os

p = ["<common-part>-<some-text-a>", "<common-part>-<random-text-b>"]
commonprefix = os.path.commonprefix(p)

new_p = [x[len(commonprefix):] for x in p]

print(new_p)

['some-text-a>', 'random-text-b>']

str1 = "hello"
list1 = ["hello1", "hello2", "hello3"]
list2 = []
for i in list1:
    list2.append(i.replace(str1,""))
print list2

[newstr.replace(str1, '') for newstr in list_of_strings]

MyList = ["xxx-56", "xxx-57", "xxx-58"]
MyList = [x[len(prefix):] for x in MyList] # for each x in the list,
                                 # this function will return x[len(prefix):]
                                 # which is the string x minus the length of the prefix string

print(MyList)

---> ['56', '57', '58']

common = "Hello_"
lines = ["Hello_1 !", "Hello_2 !", "Hello_3 !"]

new_lines = []
for line in lines:
    # Finding first occurrence of the word we want to remove.
    startIndex = line.find(common) + len(common)
    new_lines.append(line[startIndex:])

print new_lines