I cannot read this name, which is the name of one of the older sisters of my great-grandfather. It is supposed to be a german female name. This was written in 1878.
Sample of handwriting by the same guy:
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The name is Agnes.
You can compare each of the letters to those shown in this BYU Script Tutorial for German handwriting.
I extracted the relevant letters from the alphabet image on that site, and put them together in one image. I've included your image below for easy comparison.
I also found it useful to have this PDF around for comparing the letters. The benefit being you can zoom it in quite a bit:
Once you get an initial idea about what the letters are likely to be you can use the following tool to generate a sample which you can check against: