Changing name in Passport

[Terpe]

I heard that when applying for jobs, some employers prefer to have the same name in the new passport and the spouse visa. Is it possible to change the old visa name to new one? HOw much is the cost for this to have the name changed?

Not so.
Employers (like most other organisations such as banks etc) need to know that you are legally resident and allowed to work.
If you are married and using your husbands family name, they will also need to see your marriage certificate for confirmation.
When taking your husbands family name the marriage certificate is the link to your maiden name that may still showing on your passport.

My best suggestion is to decide exactly what name you will use, and be sure to keep that for all activities (National Insurance,HMRC,GP,Banks,Employment etc)
Keeping it simple will create less ID issues.