I suspect there are numerous examples of this, but I'll add Micronesia to the list. Spain had a longstanding colony in the Mariana islands from the sixteenth century, but also laid claim to other groups to the east -- the Carolines, Palau, and the Marshalls -- despite having virtually no contact with those groups. By the end of the nineteenth century, the global copra trade grew active enough for traders to begin setting up operations on an increasingly large number of islands and atolls. German corporations like Godeffroy and Sons and the Adolph Cappelle Company set up operations in the Marshall Islands, parts of the Carolines, and elsewhere in the Pacific also.

Eventually, the German government laid claim to those islands, arguing that Spain had neglected them and was acting as a poor steward. Spain argued that it's pre-existing claim to the region trumped Germany's commercial operations there. There was a brief media circus and some enthusiastic public protest in Spain and Germany -- despite the fact that surely only a few people knew anything about the region -- and the dispute was eventually settled by the Pope. Spain retained sovereignty over Micronesia, but German companies continued operating there -- until Germany acquired the region after the Spanish American War.

Ostensibly, Germany sought control of Micronesia for commercial reasons, but the islands were a drain on its treasury -- as they were when colonized by Spain and then later by Japan and the US. A vague sense that colonies were a booster for national pride really was the main factor in that acquisition.

I'd nominate Leopold II. of Belgium.

With Belgium only becoming an independent kingdom under Leopold I. in 1830 most of the good stuff had been taken already. Leopold Ii. followed his father on the throne in 1865 and he was very keen to gain some colonies despite his government's reluctance to go international, not because he wanted a powerful international empire but because he believed it would increase his relatively new country's prestige amongst the European royalty, who had their lands spread scross the globe.

At the start he had his eye set on the Philippines, who he wanted to acquire from Spain. In 1866 he tried to purchase it from Queen Isabella, when she was deposed in the Glorious Revolution in 1868 Leopold tried the same with the new Spanish monarch, Amadeo of Savoy, also unsuccessfully. Eventually he gave up on the land altogether and refocused his efforts on Africa, whose coast was already colonised to bits but still had vast unclaimed lands in its heart, which European explorers were just starting to venture into.

And because his country still wasn't too fond of his ambitions, Leopold went ahead and founded the International African Society in 1876 as his private project with his private funds (although subsidised by the country) in an attempt to establish a colony in his own free time. In 1878 he hired African Explorer and Livingston-finder Henry Stanley to start a Belgian colony in the Congo for him. In the Berlin Conference (1884/85) this Belgian colony, 76 times larger than its mother country, was officially recognised as the Congo Free State by pretty much every important colonial power.

Although it is somewhat wrong to call it a Belgian colony at that point, because it actually belonged to the Belgian Crown directly and was only taken from him by Belgium in 1908. With the rising market for rubber tyres that was very fortunate for Leopold as rubber was the main export product, but it still remains that his main intention in his hunt for a colony was not to get rich off of it but to help his international prestige along.

Im on mobile and I can't remember the source off the top of my head but I want to say that Bismarck took german colonies after the Berlin conference to maintain the european balance of power. He had few if any colonial ambitions and saw them as costly. But he also recognized that the colonial world needed balance to ensure peace (which is what the berlin conference was about). To maintain balance in the colonial world and prevent conflict in europe, germany held a few colonies in present day Tanzania and Namibia (which bismarck would later try to get rid of).

The Italian colonisation of Somaliland in the 1880's and subsequent invasions and occupations of Ethiopia in 1895 and 1936 could arguably be considered to have been undertaken for reasons of prestige rather than economic or military. As the kingdom of Italy only unified in 1861 it had been left behind in terms of colonial expansion. The territories on the horn of Africa were not particularly valuable, excepting possibly their ports to exercise influence over trade in the gulf.