Are you responsible for a utility bill that is legally not in your name?

There must be a reason that the utility company says they are responsible for the other person's bill. If it is not a valid reason, they might need a lawyer.

It doesn't matter about "legally not in your name."

If you have a group of people living at a residence, and one person skips out on the bill, you can't have a new person take things over like nothing happened. The electric company will refuse to provide service so that such game playing is ineffective.

If a house is rented, yes, the landlord can have problems with the electric company. That's why when renters move out, a landlord often will want to see proof that all the last utilities were paid. If not, they start deducting from the deposit. In many rentals, bills like electricity will simply be included in the rent so that the landlord doesn't have to worry about things getting paid.

Anyway, you haven't provided enough information about how this person you knew applied for service. Since you did not say they just moved into some new place out of the blue, I'm assuming they didn't. They're just living with a group of people who thought they could ditch a bill by changing names on the bill. Not going to happen. If the person really just moved in, they need to notify their new landlord about the unpaid bill from the prior tenants.

it is in their name or they agreed to be financially responsible for the other person

No, they are not.

If they used the electricity then they are responsible for the bill.
They can be taken to court for it.

Sorry, not enough information. Did the live there? Did they move into a new place with an outstanding bill from some anonymous stranger? Are they changing the billing?

the electric company can indeed refuse service to a residence if the previous account holder still owes money, yes. Especially if that person is STILL at that address. People used to turn on utilities, run up the bill until it was shut off, then get it turned back on in someone else's name.
While the person is not legally responsible for that bill.. the electric company is under no obligation to provide services to the residence until the previous bill is paid.


ADDED
The person is NOT being held "legally responsible". If the person was "legally responsible", then the utility company could take him to court over it.
No, you are confused. The utility company is simply refusing to provide services until the previous account for the residence is paid. The utility company could care less who pays it. They are within their right to refuse services.

They shut the electricity off to the residence. Was the other person living there at the time?