As Boo said, as long as you can prove your name when needs be for anything legal then it should be fine, maybe just a few more administrative hoops and best to keep records if possible.
What have they done as regards things like bank accounts, passports, other official things, surprises me it hasn't come up sooner.
Providing ID for anything legal or things like mortgages might need some sorting - might be an idea to get a change of name dede sorted with the circumstances drafted into it so it can be produced, if required, as a further backup.
If you have it done through a solicitor they would have to go through ID procedures, check circumstances etc... anyhow so could be useful to get everything straightened out.