There's a lot of confusion around the differences between a logo an identity and a brand, hopefully I can help simplify it.
A logo is the visual representation that your company or product uses to portray itself. An identity refers to the ways the logo is used and how it is associated with other communication elements. A brand is the impression your customers or the public forms about you or your product.
I'll use IKEA as an example. Their logo is a blue rectangle housing a yellow oval containing blue IKEA letters in a heavy slab typeface... and it's pretty recognizable throughout the world, especially for those looking to furnish with inexpensive yet stylish and functional furniture.
But IKEA's identity is more than their logo. Their stores use a massive blue facade with the large yellow letters. Their website uses a very structured grid design and makes strong use of the blue for navigation. Bright colourful photography is a key part of IKEA's identity. If you visit their brick and mortar store you'll see simple signage and pricing cards that use ample whitespace and clear uncluttered messaging. All these items are part of a highly controlled identity IKEA has utilized and refined for many years and it's all outlined in an detailed Identity Guide.
IKEA's brand is what you think about them. The impression you have of their products, their service and their reputation. These impressions are formed by your direct involvement with IKEA through visiting their stores, seeing their advertising, flipping through their catalogue or assembling their furniture. It's also formed by secondary impressions that you form from discussions with others, what you read about IKEA and even what you find on social media sites. IKEA, like many successful companies, works very hard to manage your impression.
In branding, every touch-point can inform the impression of your brand. Identifying the impression you want to portray is key. Seeing if every touch-point of your brand reinforces the desired impression is the obvious next step. It's amazing to me how few companies have every called their own switchboard or voicemail system to see what their clients deal with!
A new logo won't change your brand, but it might be a good starting point. It's always a good idea to talk to a knowledgeable designer before deciding to throw out your logo and develop a new one. Sometimes it might just need a a few tweaks, or perhaps the logo is fine but it is used poorly? That's where some identity work and an Identity Guide can help.
I never develop an logo for a client without supplying identity examples in the form of a business card, letterhead and envelope layout at a minimum.