Well, the time has finally arrived. In Girls' series finale, Hannah Horvath has officially become a mother. After Marnie uncharacteristically volunteers to help raise Hannah's child, the episode flashes forward to them co-parenting upstate, where it's revealed that Hannah named her baby Grover after all.
If you'll recall, that's the name Paul-Louis said he'd always liked when Hannah finally broke the news about her pregnancy. It may seem odd that she chose to honor the wishes of a man who declined to be a part of their child's life, but when you think about it, it's actually a very touching homage. Even if Grover never gets the chance to meet his dad, he'll always have a small piece of him to hold onto: His name.
In fact, it actually speaks more to Hannah being a good mother than fulfilling Paul-Louis' only request — something she was in no way obligated to do. It seems she realized it would mean something to Grover as he made his way in the world as a one-parent child, so she shoved aside her own predilections and put him first, even if the name occasionally serves as a painful reminder that she's standing in for two.
In fact, "Latching" was full of testaments to Hannah's strengths as a mom, whether it be her staunch determination to get Grover to breastfeed, her immediately protective reaction to her teen neighbor wandering pants-less through the streets, or the powerful, parent-praising speech she gave to the same girl after she realized she wasn't in any trouble — she was just trying to run away from home because she didn't feel like doing homework.
For a character who spent the bulk of six seasons failing to shake her own childish tendencies, Hannah has settled into motherhood surprisingly well, but it makes it all the less surprising that she named her baby Grover simply because she knew it would make him happy.