gleichnamig
same-named
Bearing the same name.
Der Film basiert auf dem gleichnamigen Roman von 1995.
The film is based on the 1995 novel of the same name.

same-named / eponymous
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same-named
Bearing the same name.
Der Film basiert auf dem gleichnamigen Roman von 1995.
The film is based on the 1995 novel of the same name.

The word is a compound of 'gleich' (same) and '-namig' (from 'der Name', name). So it literally means 'having the same name'.
In meiner Klasse gibt es zwei gleichnamige Schüler.
There are two students with the same name in my class.
This adjective is almost always used attributively, that is, directly before a noun. The predicative form ('Der Roman ist gleichnamig', the novel is same-named) is very rare and sounds unnatural.
Die Band spielte einen Song aus ihrem gleichnamigen Debütalbum.
The band played a song from their debut album of the same name.
The general meaning is used in everyday language. The meanings in music and mathematics are technical language and are only understandable in their respective contexts.
Um die Brüche zu addieren, müssen wir sie erst gleichnamig machen.
To add the fractions, we first have to give them common denominators.
In the general meaning, 'gleichnamig' (same-named/of the same name) very often refers to media or works of art that are based on another source.
Ich habe zuerst das Buch gelesen und mir dann den gleichnamigen Film angesehen.
I read the book first and then watched the film of the same name.
parallel
'parallel' and 'gleichnamig' can be confused because both can have something to do with 'gleich' (same) or 'ähnlich' (similar). But they do not mean the same thing. 'parallel' is used when two things happen at the same time, run side by side, or have a similar structure. In geometry, parallel lines do not intersect. 'gleichnamig' means that things have the same name; in mathematics, it is also used for fractions with the same denominator. For the same direction or simultaneous processes, 'parallel' fits. For the same name or the same denominator, 'gleichnamig' fits.

In der Pause hat Lisa den gleichnamigen Roman zum Film in der Bibliothek gefunden.
During the break, Lisa found the novel of the same name as the film in the library.
Die beiden Wege verlaufen parallel bis zum Bahnhof.
The two paths run parallel to each other as far as the station.