Can I specify a name for the index which SQL Server creates for my unique constraint?
Referencing the documentation for Create Unique Constraints, you should be able to use something like this:

CREATE TABLE [dbo].[Something](
    [IdentityId] [uniqueidentifier] NULL,
 CONSTRAINT [MyUniqueConstraintName] UNIQUE NONCLUSTERED 
(
    [IdentityId] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
) ON [PRIMARY]