Can company name conflict arise between two companies in different geographic market?
Short, Simplified Answer
Longer, more in-depth answer
A company only owns a trademark in the jurisdiction it registers its trademarks in. If someone has registered a company in Nigeria, they don't have to worry about being sued by the indian company in a nigerian court, because the indian company only has a trademark in India. However, this also means that the nigerian company cannot use its trademark in India because the trademark there belongs to the indian company.
However, there is something called an "international trademark", under an agreement called the Madrid Protocol, which allows you to apply for a trademark in many jurisdictions at once. India is listed as one of the member countries in the protocol, meaning that if this Indian company successfully applied through this procedure, they might have trademarks in all the countries listed.
However again, Nigeria is not listed as one of the member countries in the Madrid Protocol, therefore they won't have a trademark there nonetheless. Meaning a firm with such a trademark in Nigeria won't have to worry, until they plan on using the trademark overseas.
NB: As pointed out in a comment, two companies operating with the same name side by side may still not be a problem (at least in the EU, I cannot vouch for indian/nigerian trademark law), so long as the company that doesn't own the trademarked name infringes on the registrant's trademark (causes confusion to buyers as to who is selling the product/service)