Can I get Mom's equity line of credit put into my name after her passing?

I'm not sure how you can transfer the line of credit after your mother's death, because I don't understand your situation. You state that the you own your mother's condo. Did you own it before she died? Or did you receive ownership after her death? If you owned it before she died, how could she, and not you, have obtained a line of credit on the condo? If she obtained the line of credit while she was owner of the condo, I know of no law that requires the issuer of a line of credit to extend that credit line to the new (inheriting) owner.

On the other hand, you state that you have been making payments on the line of credit for five years. I don't comprehend why the issuer of the line of credit refuses to deal with you now"”"”except, of course, to keep cashing your checks. One possibility for you is to go higher-up in the line-of-credit organization. I've sometimes found that going to the top, or close to it, can produce favorable results. But if they refuse to deal with you, all I can see is for you to seek a new line of credit, in your name, and use some of that to pay of the old one.