As Drs. Pyatt & Cruz-Ferreira answered, the term is 'borrowing'.
We could say a bit more about this phenomenon: usually the
initial person who takes the term into the new language is
bilingual (at least partially). Depending on the speakers'
fluency in the 'lending' language, the word may be pronounced
more or less like it is in the original language. However, as the
word becomes more and more integrated into the borrowing
language, it will tend to lose distinctive phonetic aspects of
its pronunciation, and become more like 'native' words (indeed,
this process is often referred to as 'nativization' or even, in
English examples, as 'Anglicization'). Until this process has
terminated, which may take years or longer in some cases, many
borrowings will retain at least some non-native aspects (for
example, in English, word-final main stress, which is extremely
unusual in 'native' words, and so is taken by speakers as a mark
of 'foreignness', or even as a 'European borrowing'; if the word
has such marks of foreignness as final accent, speakers may even
change vowels they know are 'native' and peculiar to English,
like the [ae] in to the 'European' variant [a]; or vice
versa: if the word is the name, e. g., of an obviously foreign
person, such as the name 'Tanis' for a kid who speaks with a
Spanish accent, and pronounces his name as ['tanis], most
American kids would pronounce the name as [tuh'nis].
Obviously, there are a lot of complexities in the borrowing
phenomenon, and many linguists have analyzed borrowings from a
large number of languages into a large number of other languages,
so we know something about this phenomenon and its regularities.
Hope this helps.