I changed my name. Older qualifications under a previous name can have the name changed on them. It is unlikely they will supply a parchment in a new name, however you will be able to request an updated transcript in the new name. This was a very long process for me to achieve.
In terms of references, if you have a positive relationship with your previous employer, you can contact them and let them know that you have changed your name and they should expect to receive a request for a reference in the old name. If you don't have confidence in contacting your previous employer because of your conviction or other reason you could write to HR and notify them that your name has been changed. Your name change is, however, liable to become public knowledge.
You could also try to find employment with someone who won't check references. labouring, factory work etc. are unlikely to ask for references (think companies who hire lots of eastern Europeans). You then could build a reference with them.