For Hebrew names, one of my favorites is [name]Yona[/name], which I still believe too close to [name]Noah[/name]. 
Other Hebrew names I have heard on actual people (not necessarily babies) - that sound a little like [name]Nora[/name] to me:
[name]Abra[/name] (abe-ra)
[name]Leah[/name]
[name]Naomi[/name]
[name]Mara[/name] (mahr-uh)
[name]Raina[/name] or [name]Rayna[/name] (ray-na, rah-een-a, or rye-nah)
Other names I found in the search for names, narrowed to F. Hebrew names - that sound a little like [name]Nora[/name] to me:
[name]Jora[/name]
[name]Jola[/name]
[name]Joelle[/name]
[name]Neila[/name]
[name]Niva[/name]
[name]Dalia[/name]
[name]Dara[/name]
[name]Erela[/name]
[name]Sada[/name]
[name]Zara[/name]
I will try to think some more for other names. It looks like you are looking for a shorter name. You don’t really say how strongly or ethnically Hebrew your name is or the other names in your family that you are trying to match. I’m not saying it isn’t, but if it’s [name]Elizabeth[/name] or [name]Sarah[/name] or [name]Rachel[/name], then a [name]Cora[/name] would not be out of place.
Some names that have gained popularity throughout the culture and mix very well with other popular names from other sources. [name]Cora[/name] is not so popular at this time, but it has been, so people are apt to recognize it. [name]Noah[/name] is also currently popular and apt to be chosen for its relevance as well as despite, as well as any [name]John[/name] or [name]Michael[/name] or [name]David[/name].
[name]Noah[/name] may be a little on the edge, so that it will mix with uncommon Hebrew names as well as common, as well as names that are not Hebrew. Depending on how ubiquitous your own names might be, [name]Cora[/name] would fit in, or it may stand apart if you really would like to stick to the theme and the other names are very uncommon.
[name]Nora[/name] would have been a great name - I love [name]Nora[/name]. However, like [name]Cora[/name], it is also Greek according to Nameberry, as well as according to another source, Irish/English/Scandinavian/[name]German[/name] - not Hebrew either - based of English [name]Eleanor[/name]. You may have other references to go by. Some names are sourced simultaneously from two different languages with two different meanings, especially may be the case where the source is in another alphabet and the name has been approximated in the transliteration and relatively modern to the ears after evolving for centuries. So perhaps [name]Nora[/name] is a Hebrew name and I’m just unaware.
I think this here is a start, though. If you want a lot more Hebrew names, click on the left column “Search for Names,” tick “girls” and choose “Hebrew” from the ORIGINS menu to get all Hebrew girl names (over 300 but you won’t miss any). You can also fine-tune your search for meanings and popularity, as well as “starts with” and “ends with” and style. Good luck finding a nice match for [name]Noah[/name] and your family. 