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The rosefinches are a genus, Carpodacus, of passerine birds in the finch family Fringillidae.
The genus name is from the Ancient Greek terms karpos, "fruit", and dakno, "to bite".

1/ Scarlet finch (Mỏ to lưng đỏ, Carpodacus sipahi) 
formerly placed in the monotypic genus Haematospiza.
The species name sipahi comes from the Hindustani word sipahi for a soldier or the Anglicised form sepoy, for the red uniform worn by those in the employment of the East India Company.

2/ Common rosefinch (Sẻ hồng mura, Carpodacus erythrinus) or scarlet rosefinch
The specific erythrinus is from Latin erythros, "red".

The greenfinches are small passerine birds in the genus Chloris in the subfamily Carduelinae within the Fringillidae.
The greenfinches were formerly placed in the genus Carduelis.
The genus name is from Ancient Greek khloris, the European greenfinch, from khloros, "green".

1/ Black-headed greenfinch (Sẻ núi, Chloris ambigua)
The specific epithet ambigua is from the Latin ambiguus for "doubtful".

2/ Vietnamese greenfinch (Chloris monguilloti)
the specific epithet was chosen to honour Maurice Antoine François Monguillot, the General Secretary of French Indochina.

The Oriental grosbeaks (Eophona) are a genus of finches containing two species in the family Fringillidae.
The name Eophona is derived from the classical Greek words eos meaning "dawn" and phone meaning "shout" or "cry".

1/ Yellow-billed grosbeak, or black-tailed hawfinch (Mỏ to đầu đen, Eophona migratoria)

The genus Fringilla is a small group of finches from the Old World, which are the only species in the subfamily Fringillinae.
The genus name Fringilla is Latin for "finch".

1/  Brambling (Sẻ núi, Sẻ đồng đầu đen, Sẻ đồng họng hồng, Fringilla montifringilla) 
Montifringilla is from Latin mons, montis mountain.

The true finches are small to medium-sized passerine birds in the family Fringillidae.
The family includes the canaries, siskins, redpolls, serins, grosbeaks and euphonias,...

Fringillidae, Fringilla: Latin fringilla for finch.

Crossbills are birds of the genus Loxia within the finch family (Fringillidae), with six species.
The genus name is from the Ancient Greek loxos, "crosswise".

1/ Red crossbill or common crossbill (Mỏ chéo, Loxia curvirostra)
curvirostra is Latin for "curved bill".

The genus Procarduelis is a genus of passerine birds in the finch family Fringillidae.

1/ Dark-breasted rosefinch (Sẻ hồng Nê pan, Procarduelis nipalensis)
 formerly placed in the genus Carpodacus.

Pyrrhula is a small genus of passerine birds, commonly called bullfinches, belonging to the finch family (Fringillidae).

Fringillidae, Fringilla: Latin fringilla for finch.
The genus name was derived by tautonymy from the binomial name of the Eurasian bullfinch Loxia pyrrhula introduced by Linnaeus in 1758.

1/ Brown Bullfinch (Mỏ ngắn, Pyrrhula nipalensis)

Spinus is a genus of passerine birds in the finch family Fringillidae.
The genus name is from the Ancient Greek spinos, a name for a now-unidentifiable bird.
All of the species in the genus, except for the Tibetan serin, were formerly included in the genus Carduelis. 

1/ Eurasian siskin (Sẻ thông Siskim, Spinus spinus)
The English name is from German dialect sisschen or zeischen.