There are a couple things going on here and the comments are somewhat spread out, so let's deal with the issues one-by-one.
Tag Name - Tags should be descriptive, easy to remember, and not invite confusion.
This is a rather unique situation I think as you normally would only have the same project name for 2 different projects/libraries/languages if the 2 projects branched from each other at some time and usually one or both pick a new name at some point.
Typically when there is some naming confusion, appending a "-x" (where x is another descriptive name) to the end is appropriate. However, when this is done, it is usually best to rename BOTH projects' tags to avoid confusing users (mistagging can result in someone not seeing the appropriate questions or following the wrong tag).
- silex - Since there is another (newer) project with the same name, both of you using the same tag would be very confusing to everyone so that is out.
- silex.me - Make some sense if that is going to be your domain, but if you are a new user unfamiliar with your domain, and you see a tag "silex" and "silex.me", you might pick silex since that is your project's actual name. Again, more confusion.
- silex-live-web-creation - If a brand new users will know this is your project, then go for it. Personally, I think long tag names just take up too much screen real estate, especially on mobile devices.
- silex-web - Again, if a brand new users will know this is your project, then go for it. This is shorter and more mobile friendly. This would get my vote, but then again, I've used the word "silex" 10 more times in this answer then I've every done in my entire life, so take my opinion with a grain of salt.
Regardless of which name you pick, you still have the problems of confusion with the existing tag. To that end, I would suggest proposing a name change for that tag to something equally descriptive but less confusing for new users, like silex-framework or silex-php. Since they had the silex tag first, it would likely have to be a synonym of the newer tag, but it would force users to see something descriptive enough that confusion and mistags would be reduced.
Replacing your forums with SO - you did not ask for help on this, but you are going to get some unsolicited advice since in one of your comments you seemed confused by Wooble's comment. His follow up comment might have cleaned the confusion, but in case it didn't, you need to reconsider this idea or at least make sure you know what you are in for. From your comments here and your other post, I'm not sure you fully grasp what SE sites are about, and how aggressively we moderate questions to ensure they are on-topic and of good quality.
While other 3rd parties have tried to encourage their communities to use Stack Overflow, it is not appropriate to completely replace your existing support community with Stack Overflow. There are a number of posts scattered around, but here is a collection:
You can encourage your users to ask questions, but there need to be valid, on topic posts. Additionally, general support and bug reports have no home here, so you need to maintain another avenue for users to be able to contact the dev team directly and to be able to post and report bugs.
Android did it the proper way, but leaving all of their support forums up and just recommending questions be asked on SO.
Moving to another SE site-
Or maybe we could have the Silex tag on graphicdesign.stackexchange.com ?? – lexa 22 mins ago
That's completely up to you but you still have to be on-topic. You can't just create a tag, say "go ask questions here", and expect the SE community to accept those questions. Questions that are off-topic or don't otherwise fit withing the asking guidelines of that site are going to be downvoted, closed, and you are going to have some upset users.
Jeff's answer to one of the questions I linked above is spot on. You can't just magically create a community on Stack Overflow or another SE site. And you can't just create a tag. The questions need to exist first and you can create a tag to add to those questions. If you create a tag without questions, then the tag is just going to get deleted by the automatic cleanup that runs every 24 hours.
It is best to cultivate the site organically on an appropriate SE site, running it in parallel with your support forums and encouraging your users to ask on-topic questions on SE. Then as the SE community grows, you can reduce your support forums.