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This looks like one of a type of surname that is common in Sweden, i.e., one adapted by an ancestor which has no real meaning.
Until the beginning of the 19th century few Swedes had hereditary surnames, using a literal patronymic instead, so someone(male) called Johansson or (female) Johansdotir would be the children of one Johann, and the male's children would have his given name plus -son or -dotir.
In the early years of the 19th century the government ordered all Swedish citizens to adopt permanent family names. It must have feared that many people who end up with a few common patronymics (they did), and suggested people should create a family name of their own. A list of monosyllabic nouns drawn from nature was published, and people were encouraged to put two together to make a name.
Some of these names looked like real locative names, e.g., Eklund (oak wood)and Sjostrand (sea shore). Others made little sense, e.g., Blomkvist (flower twig).
The second component of Ramgren, 'gren' means 'branch', one of the words on the government's list. I don't know the meaning of the first component. It can mean 'paw' in Swedish, but I doubt that that's the meaning in this case. Sometimes people used a word not on the published list.