diff --git a/news/5021.bugfix b/news/5021.bugfix
new file mode 100644
index 00000000000..4de60b18e76
--- /dev/null
+++ b/news/5021.bugfix
@@ -0,0 +1 @@
+Package name should be normalized before we use it to search if it's already installed or not
diff --git a/src/pip/_internal/req/req_install.py b/src/pip/_internal/req/req_install.py
index 3b28209b1bd..d1a7b9c3de8 100644
--- a/src/pip/_internal/req/req_install.py
+++ b/src/pip/_internal/req/req_install.py
@@ -420,12 +420,16 @@ def check_if_exists(self, use_user_site):
         """
         if self.req is None:
             return
+
+        # Canonicalize requirement name to use normalized
+        # names while searching for already installed packages
+        no_marker = Requirement(str(self.req))
+        no_marker.marker = None
+        no_marker.name = canonicalize_name(no_marker.name)
         # get_distribution() will resolve the entire list of requirements
         # anyway, and we've already determined that we need the requirement
         # in question, so strip the marker so that we don't try to
         # evaluate it.
-        no_marker = Requirement(str(self.req))
-        no_marker.marker = None
         try:
             self.satisfied_by = pkg_resources.get_distribution(str(no_marker))
         except pkg_resources.DistributionNotFound: