For the record people often pay considerable money to have logos made for them, and for good reason. Also just because an icon is small/whatever you might do is low res does not make it easier, quite possibly the opposite as you have to really pay attention to what you are doing where you can afford to be slightly sloppy.
If you are doing it yourself and the online ones are not cutting it and similarly whatever passes for word art in the likes of libreoffice is also not enough then nothing is particularly likely to do it for you. The only good logo generators I have ever seen have been ones that make a parody logo of something else well known with your own text.
Spend 30 minutes learning some tricks with font design (shadows, highlights, gradients around the outside....), spend another looking at logos (there are games that make you guess what company or something), spend some more time on
https://www.fontsquirrel.com/ (or similar, do bear in mind fonts technically have licenses/copyright so make sure you can use it for commercial use if you are going down that path), and then grab copies of GIMP and Inkscape to use instead (for gimp make sure to use layers, right click on said layer in the layer window and select alpha on the text you have, now you can make new layers to fill in with various colours to achieve effects).
If you need to go hardcore pixel art there should be a few of those around as well but at least GIMP should manage there.
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