The identification of suitable response categories to allow respondents to identify their ethnicity is no mean task, not least because ethnicity itself is a term with multifarious meanings (see for example the Office for National Statistics (ONS) Guidance on Methodology.
Also, it is becoming increasingly difficult to draw inferences from nationality as to the specific religious, cultural or socio-economic environment an individual may be exposed to. Therefore a higher level of detail than first expected may be required in order for you to elicit the specific demographic information you require from your sample. Notice, for example, that on the same ONS webpage, there are links for National Identity and Religion. For completeness, you may also wish to consider these dimensions in your survey.
With a view to getting to grips with some of the central issues involved in categorizing ethnicity and what sorts of categories are suitable in different contexts, you should also find the following guide an excellent read:
Ethnic group statistics – a guide for the collection and classification of ethnicity data.
Categorizing Ethnicity by Margaret MacDougall is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.