Did Sal Hepatica get its name because the liverwort was an ingredient?

No, it did not contain liverwort (hepatica)
https://en.wikipedia.org/wiki/Sal_Hepatica

No. Sal Hepatica was so named because it was supposed to be a natural laxative salt that was beneficial to the liver, similar to another popular patent medicine of its time, Carter's Little Liver Pills. "Hepatic" means "related to the liver". Bristol Myers discontinued Sal Hepatica because it was being investigated by the FTC the same way the Carter's was (see the 1951 Time article); when the Supreme Court refused to take Carter's case (and Carter's had to drop any reference to "Liver" from its name), "Sal Hepatica" just became an effervescent laxative. As you can see from the Sal Hepatica label, "liverwort" wasn't an ingredient:

https://books.google.com/books?id=UIlMAQAAMAAJ&pg=PA1438&lpg=PA1438&dq=sal+hepatica+label&source=bl&ots=e_S0NlXwK0&sig=QBO9Hgkk6eMoG4MgoGub2z2y8hY&hl=en&sa=X&ved=0ahUKEwiZ8oKvyObOAhVCwiYKHaogAs4Q6AEIMjAG#v=onepage&q=sal%20hepatica%20label&f=false

Here's a 1946 ad for it: http://www.vintageadbrowser.com/beauty-and-hygiene-ads-1940s/115
and a 1937 one: https://www.flickr.com/photos/vieilles_annonces/4035082637/
And here's the Time article about the FTC cracking down on Carter's Little Liver Pills:
http://content.time.com/time/magazine/article/0,9171,814704,00.html