Upvote:1
Assuming you travel with both passports, you should be fine.
A name change is a fairly common event for people, particularly after marriage. Immigration will have dealt with it before.
However, you will still need to present the visa. Again this is a common enough activity, and presenting the old passport with visa, and the new passport as a valid ID, should be fine. I've done this before with two passports and a visa in the old one, and they didn't have any issue with this.
If you're concerned, bringing the documentation of your name change should provide absolute certainty.