add registration to all database

[MykolaDiachok]

I tested your project, and had a little trouble with connecting from the worked database.
Please add script to registration
DECLARE @Sql NVARCHAR(MAX) = N'';

SELECT @Sql += CHAR(13) + CHAR(10)

• 'USE ' + QUOTENAME(name) + ';

IF OBJECT_ID(''dbo.RegexSplit'', ''FN'') IS NOT NULL
DROP FUNCTION dbo.RegexSplit;

IF OBJECT_ID(''dbo.RegexSplit'', ''SN'') IS NOT NULL
DROP SYNONYM dbo.RegexSplit

CREATE SYNONYM dbo.RegexSplit FOR master.dbo.RegexSplit;'
FROM sys.databases WHERE name <> 'master';

PRINT @Sql;

EXEC sp_executesql @Sql;