To my understanding it was still self identified as the Deutsches Reich within Germany. Wouldn't it be appropriate to call it the German Empire, or the German Republic? Is there some purposeful attempt to separate the Weimar Republic from the Empire so as to distance it from Nazi run Germany?
It was still officially referred to as Germany or the German state/realm by people in high office, no one to my knowledge called it Wiemar. It got that name because in the immediate aftermath of WW1 there was ongoing violence between the various radical political groups, so when it came time for the new national assembly to meet, they choose to do it in the city of Wiemar to avoid the ongoing street fighting in Berlin.
It's a convenience term that was established to remove the ambiguity of the term "Deutsches Reich", which covers different periods. So, instead of saying "Deutsches Reich under the pre-revolutionary constitution", we say "Kaiserreich" ("Emperor Realm"). "Weimar Republic" or "Weimarer Republik", in turn, refers to the post-revolutionary period between the proclamation of the first democratic constitution in the city of Weimar in 1919 up until the establishment of the Nazis' dictatorship in 1933, which of course was yet another politically distinct iteration of Deutsches Reich.
Likewise, to distinguish pre-Unification West-Germany from the present post-Unification republic, the term "Bonner Republik" or "Bonn Republic" is often used, because Bonn served as capital during that time. This is helpful because, technically, East Germany broke up into five states which joined the (Western) Federal Republic of Germany, so it's the same constitution/state as before. "Berliner Republic" or "Berlin Republic" can be used to refer to post-Unification Germany, but it's less common, because it's simply the present and such a distinction is rarely necessary in discourse.
Translating "Reich" directly to "Empire" is problematic.
The name is used for convenience of historical discourse. The constitution of the Weimar Republic was very different from the monarchy that existed before as well as from the Hitler dictatorship and East/West Germany which followed later. So it is convenient to have a separate name for it.
In any case, the official name of the Weimar Republic was still "Deutsches Reich" - German Empire. And at the time, no one would have referred to the country as Weimar Republic - it was simply Germany.
OP is right that there is probably some purposeful attempt to separate the Weimar Republic from Nazi Germany -- in German self-awareness, there is a big line between the "good" part of the country's history (before 1933) and the "bad" part (after 1933). However, the monarchy that preceded the republic was also called Deutsches Reich, so it's not just that.
To complicate this further, the English word Empire does not have the same connotations as the German word Reich. Because of the British Empire, the English word is associated with conquest and colonialism, which does not apply to "Reich" at all. The word is basically untranslatable because its meaning is tightly tied to the history of the various German states called Reich.
BTW, West Germany from 1949-1989 is called Bonner Republik (after Bonn, the West German capital), while reunited Germany after 1989 is called Berliner Republik. Official name of both has always been Federal Republic of Germany, so the terms Bonner/Berliner Republik are used to differentiate between them in political or historical contexts.