Is there any method in content repository to get or find a block by name property?
You can use FindPagesWithCriteria
IPageCriteriaQueryService queryService = ServiceLocator.Current.GetInstance<IPageCriteriaQueryService>();
var contentLoader = ServiceLocator.Current.GetInstance<IContentLoader>();
.Select(blockReference => contentLoader.Get<IContent>(blockReference))
.Where(block => block.Name=="MyBlock")
Something like that...
Probably want to add a content reference instead to it somewhere if possible because of performance of above code...
IPageCriteriaQueryService doesn't work for blocks. Do you Episerver Find? Otherwise you have to do as Daniel suggested.