As described here: If you have a Freenode-registered nickname and want to use it from Matrix, you can do it like this:

• Leave with your nick on IRC
• On Matrix, open a new chat (Usually a “+” symbol)
• Invite @appservice-irc:matrix.org to the new chat
• Say !nick <yournick>
• A request for new chat with NickServ will pop up
• Accept it and identify yourself with your Freenode password (identify <password>)

Voila, you'll be using your Freenode-registered nick through Matrix, being able to use multiple devices simultaneously with shared history and all!