Few names I can tell are Dumbledore, Ron, Hermione & Snape.
How many others know this fact? Does the entire Gryffindor know this? I highly doubt it because this would mean the information got spread into entire school.
The following people are present when Harry puts on or takes off his Cloak, or are present when someone specifically makes reference to his possession of an invisibility cloak. I have attempted to preserve the order in which we (the reader) learn of their awareness:
Note that by the end of this book, all of the Order of the Phoenix appear to be aware of his cloak.
Note that by the end of this book, all of the Death Eaters and everyone present at the Battle of Hogwarts are aware that Harry has an invisibility cloak. By extension I think we can reasonably assume that the entire Wizarding World is aware.
The invisibility cloak that Harry has was owned by his father before Harry got it. Only a few people knew that Harry's father had it (i.e. Lily, Sirius, and Dumbledore). It was then passed down to Harry in his first year and only Ron, Hermione, Dumbledore and Malfoy know about it until the 7th book. Then Malfoy tells all of the Death Eaters so by the end many people know about the cloak.