For example: Norwegian and Danish are very close. If for some reason, Norwegian and Danish people live together in the same place, after a certain time, they'll speak the same language, will they?
Follow-up question: Can two far languages be merged? What are the conditions?
Whether Norwegians and Danes living in the same place would end up speaking 1 vs. 2 languages depends on the extent to which they remain culturally Norwegians vs. Danes, or simply generalized Scandinavians. Language is one of the most volatile distinguishing cultural features, as witnessed in North America by the loss of indigenous languages where other cultural practices are more robust, also in Scandinavia among the speakers of the southern Saami languages (Pite, Ume, South Saami) where the languages are dying out but cultural distinctness survives.
The result is typically not really a merger, rather speakers of one language shift to using the other language (the dominant language, however that is culturally determined). The "abandoned" language will probably leave some traces. As an example, the Kerewe language was introduced to Kerewe Island about 500 years ago, via immigrants from across Lake Victoria who established a centralized kingdom on the island. The number of immigrants was pretty small, and they had a substantial impact due to the new technology of centralized government. The result was that most people adopted that language: but the language that it (partially) displaced, Jita, had a number of influences on Kerewe, so that one might say Kerewe is a version of Haya-Zinza with 10% influence from Jita – not exactly a "merger". Similar (historically less-understood) language shifts affected the blending of the Pare and Shambaa where the tribe meet in the Gonja area: the dialect of Pare spoken there is substantially influenced by Shambaa, indicating that there was some interpenetration of the people. Again, the language is fundamentally Pare, with about 10% influence from Shambaa.
Something stronger than "subtle influences" may be found in creole languages, which arise in trade contexts where many cultures meet (esp. for trade purposes) and lacking a common language, a rudimentary pidgin language develops (not a language learned by children), and then this may further develop onto a full-blown language. This process involves boiling a language down to just basic vocabulary and getting rid of complicated grammar. Pidginization especially involves unrelated languages, whereas a pidgin would not develop via Kerewe-Jita contact, since the languages are similar enough that it's easy to become bilingual.
There are some examples of language merger in history. Note that such a merger is rarely a "merger of equals" where both languages contribute about the same amount to the resulting merged language.
According to this,
https://en.wikipedia.org/wiki/Pidgin
"A pidgin /ˈpɪdʒᵻn/, or pidgin language, is a grammatically simplified means of communication that develops between two or more groups that do not have a language in common: typically, a mixture of simplified languages or a simplified primary language with other languages' elements included. It is most commonly employed in situations such as trade, or where both groups speak languages different from the language of the country in which they reside "
And the most interesting part,
"Linguists sometimes posit that pidgins can become creole languages when a generation of children learn a pidgin as their first language,[11] a process that regularizes speaker-dependent variation in grammar. Creoles can then replace the existing mix of languages to become the native language of a community"
