Yes. Most international surrogacy destinations will enable the intended parents to be named on the child’s birth certificate in the country where they are born, either automatically by operation of law, or after a court process in the country of birth.
However, no international laws deals with the recognition of legal parentage between countries, so the legal position in relation to parentage is likely to vary between the country of birth and the country where you intend to live (or intended citizenship which may or not be the same as where you intend to live).
In the UK, the surrogate will be recognised as the legal mother of the child and if she’s married or in a civil partnership, unless the spouse or civil partner did not consent to the pregnancy, they’ll be the second legal parent. This is the case regardless of what the legal parentage position is in the country of birth. A parental order will usually be required in England even if you are recognised as the parents in the country of birth.