Does Sasuke have only one Rinnegan eye because he only got half of Hagoromo's chakra? To awaken the Rinnegan, you need Hagoromo's chakra, the first user of Rinnegan.

Madara had acquired Asura's chakra, which let him awaken Hagoromo's chakra. Even though the chakra eventually gets depleted, his Rinnegan still functions while it feeds on Madara's chakra. In this case now the six path chakra is not in half, it was full.

Sasuke only received half of Hagoromo's chakra. His Rinnegan also has tomoe, and consumes chakra when it's active, even without been used.  That is something which doesn't happen with the normal Rinnegan.  This suggests that Sasuke still retains the Sharingan in his left eye, yet has access to the normal powers of the Rinnegan, despite that eye not being "fully" evolved.

Because Sasuke only got half of Hagoromo's chakra, is this the reason that his Rinnegan is imperfect and in only one of his eyes?
That is partly the case. You see, Hagoromo is the son of Kaguya, the fruit of chakra. So, he is the descendant of the creator of chakra. He creates the yin release and yang release. Naruto gets the yin half, while Sasuke gets the yang half. Anybody with the yang half can get the special type of Rinnegan, called the Magatama Rinnegan (I think).