Let's analyze each question and determine the correct grammatical answer, along with explanations for why the other options are incorrect.

1. **Anna has got a job as a store assistant.**
- **Correct Answer:** store assistant
- **Explanation:** The term "store assistant" is a compound noun that correctly describes the job title. "Assistant" alone is too vague and does not specify the type of assistant.

2. **She has recently completed a course in information technology.**
- **Correct Answer:** information technology
- **Explanation:** "Information technology" is a compound noun that correctly describes the field of study. "Informations technology" is incorrect because "information" is an uncountable noun and does not take a plural form.

3. **The new name of the department which sells computers and phones is Moving Image.**
- **Correct Answer:** Moving Image
- **Explanation:** "Moving Image" is likely a proper noun used as a department name. "Moving Images" is incorrect because it implies multiple images, which may not be the intended meaning. "The Moving Images" is also incorrect because it uses a definite article and plural form, which is not typical for department names.

In summary:
1. "store assistant" is correct because it specifies the job role.
2. "information technology" is correct because "information" is uncountable.
3. "Moving Image" is correct as a proper noun for a department name.