Это выражение имеет группу захвата, которая возвращает Mike:
thisUser:\s*Your name\s*:\s*(\S+)
Демо
Test
import re
regex = r"thisUser:\s*Your name\s*:\s*(\S+)"
test_str = ("I like Apples and bananas \n"
"I like fruits and yogurt\n"
"thisUser: Your name : Mike Lewis\n"
"Email: mike@mail.com\n"
"type: Fullresopnse")
matches = re.finditer(regex, test_str, re.MULTILINE)
for matchNum, match in enumerate(matches, start=1):
print ("Match {matchNum} was found at {start}-{end}: {match}".format(matchNum = matchNum, start = match.start(), end = match.end(), match = match.group()))
for groupNum in range(0, len(match.groups())):
groupNum = groupNum + 1
print ("Group {groupNum} found at {start}-{end}: {group}".format(groupNum = groupNum, start = match.start(groupNum), end = match.end(groupNum), group = match.group(groupNum)))