Travelling to USA with passport that combines surname and given name on a single line

I am not 100% sure if I understand you correctly, so let me recapture:

• You have a valid U.S. visa, but the surname and given name appear are transposed
• Your visa is in your old passport
• In your new passport, the surname and given name are combined into your given name, and the surname remains blank

If this is the case, you should (please thoroughly read below) be able to travel to the U.S. with these documents, as can indicated by these sources:

Can I go to US with Blank Surname in Passport ? What is the problem with FNU as first name ? How does it impact my life in USA?

The fact is that, you will be able to go to US with blank First name or blank Surname in your passport, but your life gets tough afterwards

http://redbus2us.com/surname-blank-in-passport-first-name-as-fnu-in-us-visa-issues-solution/

My old passport has already expired. My visa to travel to the United States is still valid but in my expired passport. Do I need to apply for a new visa with my new passport?

No. If your visa is still valid you can travel to the United States with your two passports, as long as the visa is valid, not damaged, and is the appropriate type of visa required for your principal purpose of travel. (Example: tourist visa, when your principal purpose of travel is tourism). Both passports (the valid and the expired one with the visa) should be from the same country and type (Example: both Uruguayan regular passports, both official passports, etc.).

http://travel.state.gov/content/visas/english/general/frequently-asked-questions/about-visas-the-basics.html

This being said, ultimately, the decision to be admitted into the U.S. lies with the CBP (=Customs and Border Protection) officer at your point of entry, and you may want to temper with your chances as little as possible.

As you can see from the first link, having a blank surname in your passport can set you up for all kinds of delays and hiccups when doing official business (government agencies, banks, ...).

Therefore, I would suggest to get your passport fixed while still in your home country, and then have your visa information corrected at the US Citizenship and Immigration Services (USCIS) while you are in the U.S. if your stay requires you to get a Social Security Number or driver's license etc.

P.S.: One thing to keep in mind – the expiry date on your visa is not a sufficient measure for validity of your visa or your length of stay, as stated on the state department's website:

The admitted-until date or D/S notation, shown on your admission stamp or paper Form I-94 is the official record of your authorized length of stay in the United States. You cannot use the visa expiration date in determining or referring to your permitted length of stay in the United States.

http://travel.state.gov/content/visas/english/general/visa-expiration-date.html

My J1 visa allows me to work as an intern in the U.S. and my visa expiration date is the end of the year. The period for which I am allowed to stay, however, is determined by the DS2019. If, for whatever reason, my internship is terminated tomorrow, this will also revoke my authorization to stay in the U.S. and I will have to leave the country within a certain grace period.