I don't know anything about EF really, but in LINQ to SQL you usually express a LIKE clause using String.Contains:
where entity.Name.Contains("xyz")
translates to
WHERE Name LIKE '%xyz%'
(Use StartsWith and EndsWith for other behaviour.)
I'm not entirely sure whether that's helpful, because I don't understand what you mean when you say you're trying to implement LIKE. If I've misunderstood completely, let me know and I'll delete this answer :)
It is specifically mentioned in the documentation as part of Entity SQL. Are you getting an error message?
// LIKE and ESCAPE
// If an AdventureWorksEntities.Product contained a Name
// with the value 'Down_Tube', the following query would find that
// value.
Select value P.Name FROM AdventureWorksEntities.Product
as P where P.Name LIKE 'DownA_%' ESCAPE 'A'
// LIKE
Select value P.Name FROM AdventureWorksEntities.Product
as P where P.Name like 'BB%'
This is an old post now, but for anyone looking for the answer, this link should help. Go to this answer if you are already using EF 6.2.x. To this answer if you're using EF Core 2.x
Short version:
SqlFunctions.PatIndex method - returns the starting position of the first occurrence of a pattern in a specified expression, or zeros if the pattern is not found, on all valid text and character data types
Namespace: System.Data.Objects.SqlClient
Assembly: System.Data.Entity (in System.Data.Entity.dll)
A bit of an explanation also appears in this forum thread.