I read in Tattva Sandarbha by Jiva Goswami(verse 15) that:
skandam agneyam ityadi- samakhyas tu pravacananibandhanah kathakadivat
anupurvi- nirmananibandhana va / tasmat kvacid anityatvasravanam tv
And the names "Skanda","Agneya",etc. (by which the various Puranas
are known) refer either to those who first declared them, as is the
case with the Kathaka etc, or to those who rearranged them. Therefore,
if one sometimes hears (the Puranas) spoken of as non-eternal, it is
merely with reference to the fact that they are sometimes manifest and
The above seems one convention in naming though not always true.
Skanda purana, Agni purana, Garuda purana,
Markendeya purana, Brahma purana, Vayu Purana, Narada purana ,
Matsya purana, Varaha purana, Kurma purana. These puranas are named after their first speakers or those who repeated it later.
Shiva Purana is spoken by Lord Shiva as well as it contains glories of Lord Shiva.
Bhavisya Purana is spoken by Lord Bhava(Shiva), but I am not sure whether it gets the name because of that or because it speaks about future.
Padma purana seems to get the name because it speaks of Padma Kalpa events.
Vishnu purana speaks about Lord Vishnu spoken by Parashara.
Linga purana speaks glories of Linga.
There are various ways people interpret Srimad Bhagavatam( The beautiful story of God, devoted to god etc.) spoken by Sukadeva
Brahmanda is that in which Lord Brahma described greatness of universe.
BrahmaVaivarta puranas is spoken by Savarni Manu to Narada.
272nd chapter of Agni Purana describes different puranas as follows: