It isn't 'wrong' to name someone as Anna in one document and Anne in another. But it would be an error to confuse Anna/e with Elizabeth.
Scotland's Places lists Earlsides in the counties of Dumfries, Lanark, Peebles and Roxburgh.
If you are looking for a marriage contract, unless you are very lucky it could be a long search. As GR2 says, you would have to go to the Historical Search Room in Edinburgh (or hire a professional searcher there). Marriage contracts are not usually in the Register of Deeds for the year of the marriage, because they may not be registered until something happens to make it necessary to register it, for example the death of one of the couple.
There are (mostly handwritten) indexes to the Registers of Deeds for some years, but I cannot tell you offhand which years in the 17th century have been indexed.
If you have checked all the available indexes and still not found the one you are looking for, you then have to look through all the deeds for the missing years. These are recorded chronologically by date of registration, and each clerk kept his own register so for many years there are two or even three volumes to go through.
There is always the possibility that the marriage contract was not registered at all, or that it has found its way to some other place than the National Records of Scotland, such as a local or a university archive.
(I have been looking sporadically, and so far unsuccessfully, for about 10 years for a deed which I know was dated 14 June 1725, because it is referred to in the testament of David Wyllie who died in 1757, and as an eik dated 1 June 1757 to the testament of his brother James Wyllie who died in 1744. Therefore the deed had not been registered by 1744, but it was registered by 1757. There are no indexes to the Registers of Deeds for most of these years, and there were three clerks at the time so there are three sets of volumes to plough through.)