Here are some name suggestions for a male woodcutter cartoon character, offering a range of styles:

Rustic & Traditional:

• Barnaby Timber
• Silas Oakheart
• Jedediah Axehand
• Forrest Strongarm
• Grizzly Hacket
• Elderwood
• Hawthorne
• Burl
• Asher
• Chip

Strong & Powerful:

• Magnus Timberfall
• Ragnar Stonehand
• Boulderfist
• Ironwood
• Stoneheart
• Cliff
• Ridge

Whimsical & Fun:

• Woody Woodpecker Jr. (a playful take on a classic)
• Splinter
• Chuck
• Twiggy (ironically, for a strong character)
• Knotty
• Sawyer

Mysterious & Intriguing:

• Shadow Axe
• Whisperwind
• Nightwood
• The Carver

Modern & Edgy:

• Jax
• Ryker
• Cole
• Wren

Consider combining elements from different categories to create a truly unique name. For example, "Barnaby Stonehand" blends a rustic feel with a sense of strength. You can also add a descriptive middle name or surname to further enhance the character's personality. For instance, "Silas Oakheart the Wise" or "Forrest Strongarm the Bold."