There are several synonyms for the phrase "having a good background." Some options include having a strong foundation, having a solid footing, having a good base, or possessing a sound understanding. Other possibilities include being well-versed, experienced, knowledgeable, or proficient in a particular area. Additionally, having a good background can also be synonymous with having a respectable reputation or being highly regarded. Ultimately, the phrase describes someone who has a thorough understanding and expertise in a given subject, which can be demonstrated through their educational or professional background, as well as their personal attributes and abilities.