The lease doesn’t need to be in your name to register your address (empadronarte) — but how you actually live in that home matters a lot for figuring out which document you need.
If you live with someone who does hold the title
The titleholder (the owner, or the tenant whose name is on the lease) has to sign an authorization, and provide their ID along with proof of their title over the home — the deed, the lease, the property tax (IBI) receipt, or a utility bill in their name at that address.
If you don’t have that authorization
It’s common for a utility bill in your own name at that address to be accepted as an alternative. Some town halls also accept other documents depending on your situation — a work contract listing that address, a minor dependent’s school enrollment certificate, or a social-services report.
If you own your home or the lease is in your name
The deed or lease, plus a utility bill in your name, is enough — the simplest of the three cases.
A separate case: no fixed address
If you have no address to register at all, there’s a different route through your municipality’s social services — it’s not a document-preparation process like the ones above, but direct coordination with those services.
The fee
There’s no national fee for registering — it’s free in most town halls (confirmed, for example, in Barcelona). Some do charge for issuing the paper certificate, so it’s worth confirming with your specific town hall.
Verified against consistently-corroborated gestoría and legal-portal sources specializing in Spanish immigration, since municipal registration is a town-hall competence and no single official national information sheet exists for this procedure.