Gray Wake, Bam's tattoo artist, tells TMZ ... the former "Jackass" star came with a friend into Tribal Roots Tattoo Studio last week in Escondido, CA -- looking to grab a new tat.

He says he recognized Bam instantly because he grew up watching the series, but didn't know ahead of time he was coming in. Gray tells us Bam wanted his son's name, Phoenix, above his eyebrow, and he wanted it written in Arabic.

We're told Bam already had the design on his phone, Gray helped him out with the placement, and then they just went for it. He also got a small tattoo on his hand.

As you know, Bam's been dealing with problems lately on multiple fronts ... his wife Nikki Boyd filed for legal separation in February, calling it quits after she claimed Bam had a non-sober visit with Phoenix.

He was also arrested earlier this month for domestic violence after allegedly kicking a woman. Law enforcement said the victim referred to Bam as her "husband" -- although our sources told us it was NOT Nikki, but rather his current girlfriend. The D.A. told us he would likely not be charged.

BTW -- looks like Bam also got a matching stomach tattoo with a fan after his face and hand ink ... so he's apparently on a tat spree right now.