Python3: Can use other than 'self' as a 1st parameter of methods?

Can this code

class Point:
    def __init__(self,x,y):
        self.x=x
        self.y=y
    def __str__(self):
        return "Point({},{})".format(self.x,self.y)
p=Point(3,5)
print(p)

be modified to following code?

class Point:
    def __init__(p,x,y):
        p.x=x
        p.y=y
    def __str__(p):
        return "Point({},{})".format(p.x, p.y)
p=Point(3,5)
print(p)

It seems to be worked in this case. But it is so naive case. I wonder using other than 'self' will cause some problem in some situations.