From the quotation below (the source for which I have lost), it looks like Rambo may refer to a hill or mountain with ancestral connections. But read further for an explanation as to why some might think the name Rambo was "created".
"His [Peter Gunnarson Rambo's] Burial Record "Four pages of death records from the church at Wicaco were found by Peter Craig, whom I regard as the world's foremost historian of the earliest colonists settlers on the Delaware. They were in the Amandus Johnson papers (box 69, folio 6) at the Balch Institute in Philadelphia, and had been copied prior to 1800 by Rev. Nicholas Collin from the now long-lost Gloria Dei (Old Swedes) churchbook of 1697-1750. Under the list of 'Fode i Sverige' (born in Sweden) was an entry in Swedish: 'Peter Rambo of Hisingen, 85 years and almost 8 months [old] buried 29 Jan 1698, married 7 April 1647 - 12 Oct 1693, had 4 sons and 3 daughters ..... Brita Matsdotter.' "From the entry, we have concluded that Peter Rambo was from Hisingen, an island formed by the Gota River, and now part of the city of Gothenburg, in Bohus & Gothenburg province, Sweden. It would seem that Peter was born about Jun 1612, and his wife, Brita died 12 Oct 1693. ... "We already knew that Peter's sister lived in the Gothenburg, Hisingen area in 1693 when she asked the postmaster of Gothenburg to inquire in his letter to America about her brother Peter Rambo. At that time, Hisingen was divided into an eastern and a western hundred: the western part of Hisingen was ruled by Norway until 1658, while the south-eastern hundred had always been part of Vastergotland in Sweden. (Historisk-Geograf-iskt och Statistiskt Lexikon ofver Sverige, Vol. III, pp. 341-43, Stockholm, 1962). "There is a hill in Hisingen called Ramberget - Raven's Mountain - with a panoramic view of the city and harbor of Gothenburg. The presence of the hill called Ramberget lends more credence to the statement by PGR's grandson Jacob Bengtsson (see Benson, Peter Kalm's Travels, p. 730) that his grandfather was first called Peter Gunnarson Ramberg and was from Vastergotland, but later changed his name to Rambo." (573),, with corrections) Beverly Rambo believed the name Rambo is Swedish in its origin and meaning. Dr. Bengt Wennberg, professor of languages at Drexel University, conferred with Swedish Rambos, and concluded that the literal meaning of Rambo was "home of the raven".(9) In Swedish, the word or suffix "bo" means home or dwelling. Thus, "rambo" might refer to the raven's nest or to a person's home located on the hillside, or side of the mountain."
The alternative logic:
Prior to the British takeover of the New Netherland colony, Dutch, Swedish, and Finnish and Palatine families mostly used a patronymic naming system, meaning each new generation was known by the father's given name. Thus, the original immigrant from this family was Pieter Gunnarsen, or "Pieter, son of Gunnar". His father, in turn, was called Gunnar Pietersen, meaning Gunnar's father was named Pieter.
This system, coupled with patterns for the selection of given names, served families for centuries, but was evidently unsatisfactory to the new British administrators. Sometime in the last quarter of the 17th century, the Brits required that all of their new subjects have a surname. I have read of a "edict" to that effect, but have never seen direct evidence of the form or date of the requirement. But records from former Dutch communities show convincingly that by 1700 people had pretty much adopted surnames. It also appears that senior generations may have been excepted, because there are a number of colonists whose sons used a surname, but the father is never known to have done so.
Families appear to have been given free choice as to the names they used. Many took the name of their ancestral homes, hence the large number of Dutch families named Van-Someplace, as "van" means "from". Another very common method was to take the given name of the American patriarch; had the Rambo family done this, they would be called Pietersens. One early immigrant Claes Cornelissen (aka Van Schouw), had at least three sons who were adults before the British takeover; his grandchildren used their respective fathers' names, giving rise to American surnames Clawson (for son Claes Claesen); Pieterson (for son Pieter Claesen); and Garrabrant (for son Gerbrant Claesen). Others took occupational names, like De Kuyper (cooper, or barrel maker). Still others seem to have selected wholly new names--of my ancestors, Cadmus and Vreeland appear to fit this done this.
The "Ramberget" story is is logical, although it doesn't really tell us when the name was adopted. Even if the name comes from Raven's Hill, I would tend to think that it was adopted under the English edict, unless evidence emerges showing that Rambo was used as a surname prior to the British takeover and/or in primary records from Sweden--Peter's baptismal record, for example. Note that the record that shows him as "Peter Rambo of Hisingen, 85 years", etc. may not reflect the original characterization of his name. His marriage record, presumably from America, would be telling as well, but it appears to have been lost.
As to your other question, "Mattsdotter" likely means Brita's father's given name was the Scandanavian equivalent of Matthew.
Hope this helps,