There's not much you can do... this is why you have a good backup strategy in place (and, ideally, don't execute any "ad hoc" t-sql in a production database before testing in a test database, then copy/paste the statements to help avoid these types of errors in the future).
Pulling info from the comments, you can start off by doing something along these lines: Can I rollback a transaction I've already committed? (data loss)
(this is for PostgreSQL, but the idea is the same... stop the server, backup all relevant files, etc).
If you have transaction logging and log backups, you can attempt a point in time restore, but this must be set up prior to your error. See here: Reverse changes from transaction log in SQL Server 2008 R2?
Your best bet in this case may be to spend some time working on resolving without restoring. It looks like you updated your customer names. Do you have another source for customer information? Can you compile an external list of customers and, say, addresses, so you can do a match on those to reset your db's customer names? If so, that might be a much easier route, getting you most of the way to a full recovery of your bonked field. If you don't have a ton of data, you can do this and fill the rest in manually. It's a process, but without a good backup of the db to revert to, it may very well be worth looking at...
Also note that if the database is hosted on a cloud based S/P/Iaas, you may have deeper level backups, or in the case of "SQL Database" (e.g., SQL Azure), point in time backups are set up out of the box even for the lowest service plans.