Specifying names of variables in output of self.coordinate_ring()

edit

Let

E = EllipticCurve([1,2,3,4,5])

Then E.coordinate_ring() outputs a ring with generators.

E.coordinate_ring().gens()

yields

(xbar,ybar,zbar)

Is there a way to change the names of these variables at any point in this process?

EDIT The goal is to have sage treat the underlying rings to be treated as unique objects. Currently if I execute

E1 = EllipticCurve([1,2,3,4,5]).coordinate_ring() 
E1._names = ('a','b','c')
E2 = EllipticCurve([1,2,3,4,5]).coordinate_ring() 
E2._names =('l','m','n')
E1;E2

I get

Quotient of Multivariate Polynomial Ring in x, y, z over Rational Field by the ideal (-x^3 - 2*x^2*z + x*y*z + y^2*z - 4*x*z^2 + 3*y*z^2 - 5*z^3)
Quotient of Multivariate Polynomial Ring in x, y, z over Rational Field by the ideal (-x^3 - 2*x^2*z + x*y*z + y^2*z - 4*x*z^2 + 3*y*z^2 - 5*z^3)

(An indication that the rings are "the same":

E1sing = E1._singular_()
E2sing = E2._singular_()

ProdE1E2sing = singular.ringtensor(E1sing,E2sing);
ProdE1E2.sage()

gives

Quotient of Multivariate Polynomial Ring in x, y, z over Rational Field by the ideal (-x^3 - 2*x^2*z + x*y*z + y^2*z - 4*x*z^2 + 3*y*z^2 - 5*z^3)

whereas there should be 6 variables if the two rings were unique.)

Note: I have also tried to change the _gens, as well as injecting variables at every stage, but all with the same outcome.