Name of double sided search algorithms
What you have implemented is a variation of bidirectional Dijksktra's algorithm.

Bidirectional search is a graph search algorithm that finds a shortest path from an initial vertex to a goal vertex in a directed or undirected graph. It runs two simultaneous searches: one forward from the initial state, and one backward from the goal, stopping when the two meet. When each search is Dijkstra's algorithm, we end up with bidirectional Dijkstra's algorithm.

In which order the algorithm should expand the search in each direction and in which efficient condition the algorithm can stop the search are two obvious and critical factors for a bidirectional search. They are studied in quite a few papers.

It looks like there is not a special or specific name for the variation of bidirectional Dijkstra's algorithm that expands the search from the side whose front is nearer to its starting points. One reason to explain away the lack of a name is that it is not easy to argue that strategy should offer a nicer heuristic when compared to other strategies.

You may want to read the Wikipedia article on bidirectional search.