There’s a few ways of doing this, but perhaps the easiest is to use custom CSS to override the Read More label already there (but hidden for screen readers). It also depends on which blog style you are using.
Example Overide:
.blogstyle1 span.screen-reader-text {
width: 100px;
height: 20px;
clip: auto;
}
That is if you are using the first blog style, but change it if you are using another. It also greatly depends on if you are using excerpts for your summaries. IF so, then things will get a lot more messier/complicated to overide it.