(?<=^University\s).+

"Park, Los Angeles"

 "Los Angeles"

 (?<=, ).+

  
>>> import re
>>> 
>>> text = 'University Park, Los Angeles'
>>> 
>>> match = re.search(r'^University [^,]+, (.*)', text)
>>> if match is not None:
...     match.group(1)
... 
'Los Angeles'
>>>

 df['RegionName1'] = df['Temp'].str.extract('((?<=^University\s[^,]).+(?=\())')

 "University Park, Los Angeles (University of Southern California)"

 ark, Los Angeles

 df['RegionName1'] = df['Temp'].str.extract('((?<=^University\s[^,]+).+(?=\())')

  
>>> import re
>>> 
>>> text = 'University Park, Los Angeles (University of Southern California)'
>>> 
>>> match = re.search(r'^University [^,]+, (.*) \(', text)
>>> if match is not None:
...     match.group(1)
... 
'Los Angeles'
>>>