Use str.split:
string.split(s[, sep[, maxsplit]])
Return a list of the words of the string s. If the optional second argument sep is absent or None, the words are separated by arbitrary strings of whitespace characters (space, tab, newline, return, formfeed). If the second argument sep is present and not None, it specifies a string to be used as the word separator. The returned list will then have one more item than the number of non-overlapping occurrences of the separator in the string. If maxsplit is given, at most maxsplit number of splits occur, and the remainder of the string is returned as the final element of the list (thus, the list will have at most maxsplit+1 elements). If maxsplit is not specified or -1, then there is no limit on the number of splits (all possible splits are made).
full_name = "My Name".split()
It will return a list:
In [1]: full_name = "My Name".split()
In [2]: full_name
Out[2]: ['My', 'Name']
To assign the first and last names to variables you can unpack:
In [3]: full_name = "My Name"
In [4]: first, last = full_name.split()
In [5]: first
Out[5]: 'My'
In [6]: last
Out[6]: 'Name'