Appearing on search results is not luck, LinkedIn uses a set of internal algorithms that allow optimized accounts to rank better.
The most important way to rank higher on search results is to have a complete profile. Make sure your name on the profile is the same you use when you introduce yourself at networking events, fill all aspects of description, education and job information.
If you still do not know if the profile is complete, LinkedIn provides a helpful tracker which appears at the top and on the side of your profile page after you click edit,it indicates the information you should add.
After completing your LinkedIn profile, don´t forget to include keywords that you want associated with your name. For example, if you are a digital marketer, you can include words like marketing, e-marketing, digital marketing or social media in your background section, in skills and experience and in the education section.
Another way to rank higher on search results is to participate in LinkedIn Groups. If you do not have many contacts, it is a great idea to join groups and increase the level of activity of your profile; it can also give you exposure among other industry members.
Search LinkedIn using topics related to your industry and check where people in your network are involved too. Try to contribute in a professional way to the topic being discussed and engage as much as possible.