"Matins" was traditionally sung overnight, or in the very early morning. The name comes from the Latin "matutinae" which means "morning [hours]". In the 1960s,with a revision of the Divine Office, Matins was removed from those hours which must be sung (or said). It was renamed "The Office of Readings", and is permitted to be used at any time.
Lauds was traditionally the first Office sung after getting out of bed. A selection of mostly praise psalms, the name comes from the Latin "laudes", which means "praises". It is now generally combined with the immediately following office, Prime.
Vespers, sung in the evening before dinner, comes from the Latin "vesperae", meaning "evening [hours]".
Compline, at the ending of the day just before bed, comes from the Latin "compleri", "to fill up" (also the source of our word "complete").
The other offices, Prime, Terce, Sext, and None (pronounced with a long "O"), were sung traditionally at about the first, third, sixth, and ninth hours after sunrise - about 7 AM, 9 AM, noon, and 3 PM. The words come from the Latin for those ordinal numbers - "prima", "tertia", "sexta", and "nona". "Nona" is indeed the source of our word "noon", even though it refers to the 3 PM prayer. Etymonline.com states:
Sense shift from "3 p.m." to "12 p.m." began during 12c., when time of Church prayers shifted from ninth hour to sixth hour, or perhaps because the customary time of the midday meal shifted, or both.