from collections import Counter

lst = [["Sam", "John", "Alex", "Sam", "Alex"], ["Max", "Sam", "Max"]]

print(list(map(Counter, lst)))
# [Counter({'Sam': 2, 'Alex': 2, 'John': 1}), Counter({'Max': 2, 'Sam': 1})]

count_list = []
for l in list :
    d = {}
    for str in l:
        if str not in d:
            d[str] = l.count(str)
            count_list.append(d)

count_list = []
for l in list :
    d = {}
    for str in l:
        if str not in d:
            d[str] = l.count(str)
    count_list.append(d)