There's a great new website developed by the Ainmean-Àite na h-Alba, which is apparently a national advisory partnership for Gaelic place-names in Scotland, whose purpose is to agree correct forms of Gaelic place-names for maps, signs and general use.
You can search for a place name in English or in Gaelic, or by other criteria, location, type of name, local authority, parish post 1891, county post 1891
old admin area, topographical feature type, post town, OS sheet number, OS grid reference, nearest main road, post code.
So search for Melrose, and you find out that the Gaelic name is Maolros, and that it means bald moor. It tells you that it's in the Scottish Borders, too, and there's a link to the OS map.
For some names, it discusses the etymology of the name, and the forms shown in various dictionaries and reference books, and for some (though not for Melrose) there's an audio file giving the Gaelic pronunciation.
Using the advanced search, you can type in the name of a local authority, and get a list of all the places there; at the moment, the only place in the Scottish Borders listed with a Gaelic name is Melrose. I was surprised not to see Kelso/Cealso or St Boswells/Naomh Boisil, but perhaps they'll get on there. There are a number of other places in the Borders that have place names that could have Gaelic origins, and many more with Brythonic origins.
There's an A to Z of English place names only which is a bit odd, I think there should be an A to Z of Gaelic place names, too.
At present there are only 1,000 entries covering places throughout Scotland, but they say that work will continue to add further research and sound files to assist with pronunciation, and to expand the number of entries, and you can also write in with suggestions and queries There's also a page where you can apply for a number of leaflets and maps, most of which are free, and post free in the UK. They have a blog, too, and people have put suggestions on the blog too.