any idea about recognition by DR Ministerio y Policia new familly name

First of all, just try again.  Different person, different perspective.  The one you talked to probably has no idea of what they are asking or why...just the way it is...only my opinion.  If that doesn't work, there are several more avenues to pursue...

I did try several times - she is so dummy

Get a damm good lawyer with some pull honey!

I know but it cost money - and it is for nothing just for dummy person in this office

is there any higher department that I could appeal on my own

Ot may cost but they usually have contacts to bypass the problem people!!

so everything in DR has to be done by lawyers - meaning that they are corrupted as well lol

anyway thanks for suggestion

Doesnt have to be. You can continue to hit your head against the wall.

and do you have any suggestion what should I do with bypassing lawyers or this site is the good commercial for lawyers only??? In normal countries you can fix simply issues by yourself

@ Luda Problems with name changes abound in every country. We have the same type of problems wherever we go as my wife still uses her maiden name as cannot pronounce or remember the spelling of my name. Also to change her name requires her to present her passport in her own country and then as it is a new passport the name change will not match the old passport which carries her residency certificate which cannot be changed to her new passport. Therefore for all officialdom she is known as Miss but married which always flags up as an error and often causes us problems with movement as frontline beaurocratic staff only work to one paragraph . If it does not fit it gets rejected.
The main reason for rejection is why are name differences/ changes. Many will attempt this to hide a past. You will usually find that a letter and small in person appointment to explain. This can work as long as you are not hiding anything. Transparency is always best.

thank you for your suggestion but I did try to explain and I provided all documents for it and this lady in this office is so dummy - that why I have post it here to find another solution to go to the higher person in some government places or maybe by the court to recognize my "new" name - I am not sure where to go
I got previous suggestions take lawyer - I do not need that solution because I did all papers by myself and I was told after the exam I am already citizenship I just need to be sworn. Taking lawyer everyone knows this is a last solution - and they are corrupted in DR - I read previous posts here and planner is suggesting to them lawyers and btw I have called one of them and he wants crazy amount for it and he said no guarantee.
I feel this site is a big commercial for lawyers
Thank you all for your time and your kind suggestions

Try to bypass this particular person and find out exactly what the problem is. We had similar problem recently with Chinese Embassy as to whether my son needed a visa or travel document. To and thrower between departments until I berated loudly enough in very poor mandarin about going to British embassy to a supervisor. Suddenly no problem travel docs issued same day

I am sorry you are not having success. I have not other suggestion for you. This is just not like any other country.

I know how it is there I was living there for 7 months and everything is possible if you are there - right now I am trying to solve that from Canada I just need to know the higher office to go to complain

No idea at all.

i would get a good dominican immigration lawyer if you dont already have one.
if he cant help you i see no other choice but to do what they want here.

You pay the lawyer, the lawyer pays the burocrat, it gets done. 
Or, if they don't care about the name, just ignore the whole thing.