Canonically speaking, you can only change parishes by moving out of the parish boundaries. You can of course attend another parish church for the Mass, and even sign the registry, but canonically speaking, you will always belong to the parish church nearest you. .
That is true only for Territorial Parishes. Under Canon Law, a parish can be erected as a ‘Personal Parish’. Those do not have territorial boundaries (technically, they are limited only by the diocese) If they are accepted by the pastor at a personal parish, they are no longer Canonically attached to their territorial parish, but are under the pastoral care of the pastor of the community entrusted to him by the diocesan Ordinary. (Canon 519)
Canon 519 places Canonical pastorship based on the community entrusted by the bishop
Can. 519 The pastor (parochus) is the proper pastor (pastor) of the parish entrusted to him, exercising the pastoral care of the community committed to him under the authority of the diocesan bishop in whose ministry of Christ he has been called to share, so that for that same community he carries out the functions of teaching, sanctifying, and governing, also with the cooperation of other presbyters or deacons and with the assistance of lay members of the Christian faithful, according to the norm of law.
So a bishop might create a parish “St. Whoever” and entrust the community that lives in the area from 7th Ave to 32rd Street and between Main and Elm St. All Catholics in that area (technically, all Baptized Christians) belong to that parish.
The bishop might create another parish, “Our Lady Queen of Everything” and entrust the Esperanto speaking community to that parish.
So an Esperanto speaking person who live in the boundaries outlined for St. Whoever is a member at that parish, UNLESS they go to the pastor of OLQoE and ask him to be their pastor, in which case he truly does become their Canonical pastor.
Personal Parishes are most commonly erected to serve a specific ethnic or linguistic community, but could be established for any just reason as seen fit by the diocesan Ordinary. (Canon 518)
Here in Detroit, not only are there several ethnically based personal parishes ( the nearest parish to me is actually a Polish ethnic personal parish, staffed by priests from Poland and most of the Masses are in Polish). So yes, even though it is the closest parish to me, I am not a member there, as it does not have geographical boundaries,; but a Polish person 20 miles away could be under the Canonical authority of the pastor there.
In addition, two of the parishes that serve the EF community are designated as personal parishes. So the members of those, no matter where in the Archdiocese they live, are Canonically members of those parishes as well.